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That some stretches of freeway in Germany do not have speed limits is more than a well-known fact, it's legend. Videos of folks filming themselves doing outrageous speeds on stretches of the Autobahn are, shall, we say, not uncommon.

One recent video posted online has, however, sent authorities into a tizzy. The owner of a Bugatti Chiron went beyond the bounds of reason. Way beyond. The man drove his car at up to 417 km/h on a stretch of the Autobahn A2 between Berlin and Hanover.

The German Ministry of Transport has criticized the high-speed stunt, carried out by a Czech millionaire aboard his Bugatti Chiron.

Accompanying the video is an explanation by the driver, who writes that the video was filmed last year on a straight, three-lane, 10-km section of highway and that visibility was excellent along the entire stretch. "Safety was a priority, so the circumstances had to be safe to go", he explained.

Still, the Chiron can be seen passing several vehicles. It's worth noting the commendable discipline of German drivers, who are not in the habit of changing lanes without first checking the surrounding traffic. However, not everyone can see a vehicle coming at over 400 km/h.

Authorities in Germany are obviously aware that their highway network includes sections without speed limits, but the Ministry of Transport said in a statement Wednesday that it "rejects any behavior in road traffic that leads or can lead to endangering road users".

It added, citing the country's road traffic laws, that "All road users must comply with the rules of the Highway Code... every person must behave in such a way that no other person is harmed, endangered or inconvenienced more than is unavoidable in the circumstances."

The Ministry noted that the law also requires drivers to operate at a speed that ensures the vehicle is under constant control.
Shopicar.com, 100% online, shop for your next car, buy online and get it delivered to you anywhere in Quebec!
It's clear that at 300 or 400 km/h, a vehicle can put the lives of others, as well as the driver themselves and any passengers, at great risk. The man behind the stunt said that his faith was a precious help in the realization of his feat... in addition to his driving skills.

Might this video create enough momentum to change the law? In Germany, many have been calling for years for the abolition of highway sections without speed limits. During last year's election campaign, the Green Party, now a minority partner in Germany's coalition government, called for a 130 km/h speed limit on the motorway network as part of efforts to reduce the country's carbon dioxide emissions. However, this idea was dropped as a result of negotiations to form the new government.

Unsurprisingly, though, every time a video like this is released, the debate is reignited. Will we ever see speed limits on the stretches of road that don't have them?

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bugatti hub-news auto123 germany bugatti video chiron

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A Bugatti Chiron filmed moving at 417 km/h on the Autobahn | Car News | Auto123

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That some stretches of freeway in Germany do not have speed limits is more than a well-known fact, it's legend. Videos of folks filming themselves doing outrageous speeds on stretches of the Autobahn are, shall, we say, not uncommon. One recent video posted online has, however, sent authorities into a tizzy.

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2b) Relating Fractions, Decimals, and Percents

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2b) Relating Fractions, Decimals, and Percents

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How to find percentage (tutorial) | Arithmetic (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Show 109% by shading. So just as a bit of review, 109% if we were to write it out, would literally be 109 percent, which is the same thing as 109 per-- and I could write cent again, but that's getting old. Cent means 100, so it literally means 109 per hundred. If you had 100 per 100, you're dealing with the whole, but now we have more than a whole. We have 109 per 100. We can actually write this as a ratio, or as a fraction. This is the same thing as 109 per 100. It's the the same thing as 109/100. So let's shade that in. So we have a whole here, so we could consider this square a whole. In the last video, we counted. This is a 10 by 10 square. It is cut up into 100 pieces. So if we want 109 of those 100 pieces, what are we talking about? That means we're going to shade in all of the 100 right over here. Let me do that in a new color. So we'll shade in all of this. If you just shaded that in, that would be 100%. That would be 100/100, or 100 per 100, or 100%. I think you're getting the meaning of all of this. I don't just want you just memorize this stuff. This really just means 100 out of 100, or a whole. And you can see that this is the whole square. That's 100 out of 100 right there. The question is saying show us 109% by shading. We already did 100 per 100, but we need to do another 9, so let's shade in another 9. So now we have one, two, three, four, five, six, seven, eight, nine. So this piece right here, you could almost view that is-- well, that is! That is 9% of an entire square. This is 100% of an entire square. If you considered this whole thing plus this blue area right over here, you are talking about 109% of one whole square. Hopefully, that made sense.

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Meaning of 109% (video) | Intro to percents | Khan Academy

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Show 109% by shading. So just as a bit of review, 109% if we were to write it out, would literally be 109 percent, which is the same thing as 109 per-- and I could write cent again, but that's getting old. Cent means 100, so it literally means 109 per hundred.

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The meaning of percent (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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The "Unit Price" (or "unit cost") tells you the cost per liter, per kilogram, per pound, etc, of what you want to buy.

Just divide the cost by the quantity:

Example: 2 liters for $3.80 is $3.80/2 liters = $1.90 per liter

Example: What is best

2 liters of Milk at $3.80, or

1.5 liters of Milk at $2.70 ?

In this case the "Unit" is 1 liter, and the Unit Prices are:

$3.80 / 2 liters = $1.90 per liter

$2.70 / 1.5 liters = $1.80 per liter

So the lowest Unit Price (and the best bargain) is 1.5 liters at $2.70.

Example: What is best

10 pencils for $4.00, or

6 pencils for $2.70 ?

Here is the Unit Cost:

$4.00 / 10 = $0.40 per pencil

$2.70 / 6 = $0.45 per pencil

So the lowest Unit Price (and the best bargain) is 10 pencils for $4.00

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The "Unit Price" (or "unit cost") tells you the cost per liter, per kilogram, per pound, etc, of what you want to buy. Just divide the cost by the quantity: Example: 2 liters for $3.80 is $3.80/2 liters = $1.90 per liter Example: What is best 2 liters of Milk at $3.80, or 1.5 liters of Milk at $2.70 ?

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A comparison of two related quantities.

Often the second quantity is time (per second, per hour, etc) but it can be anything.

Can be in the style "this per that" or as a single number calculated using division.

Example: Sam makes 3 pancakes every 6 minutes, that is a rate of:
* 3 pancakes per 6 minutes
* 0.5 pancakes per minute
* 30 pancakes per hour
* an hourly rate of 30
* etc

Example: 200 sausages were eaten by 50 people. that is:
* 200 sausages per 50 people
* 100 sausages per 25 people
* 4 sausages per person
* etc

Example: Alex invested $100 for a month and made $3
* the interest rate is 3/100 = 3% per month
* etc

When we compare to a single unit quantity we call it a Unit Rate.

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A comparison of two related quantities. Often the second quantity is time (per second, per hour, etc) but it can be anything. Can be in the style "this per that" or as a single number calculated using division.

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If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Video transcript

let's do some example questions dealing with ratios so we're told the table shows the number of people waiting in line for different rides at an amusement park so 15 people are waiting in line for the roller coaster four people for the slingshot twelve people waiting in line for the bumper cars and eleven people in line for the roundup what is the ratio of people waiting in line for the roundup to the people waiting in line for the slingshot pause this video and see if you can figure it out so we want to know the ratio of the people waiting in line for the roundup this is the roundup right over here to the right to the number of people waiting in line for the slingshot so there's 11 people waiting in line for the roundup and there are four people waiting in line for the slingshot so the ratio is 11 to 4 or for every 11 people in line for the roundup there are 4 people waiting in line for the slingshot let's do another example Katie loves to read in the last few months she has read three graphic novels two mysteries for science fiction novels and 21 comic books what is the ratio of sci-fi novels to comic books so once again pause this video and try to work it out on your own all right so we want to know the ratio of sci-fi novels so she has four sci-fi novels the ratio of that to comic books she has 21 comic books so the ratio is for every four sci-fi novels she has 21 comic books don't do that that other color she has 21 comic books so the ratio is 4 to 21 the ratio of sci-fi novels to comic books for sci-fi novels for every 21 comic books let's do one more example this is strangely fun what is the ratio of apples to bananas pause this video and try to figure it out so let's see there are 1 2 3 apples so for every 3 apples how many bananas are there well there is 1 2 3 4 bananas so the ratio of apples to the ratio of apples to bananas is 3 apples for every 4 bananas in order matters if they set the ratio of bananas to apples then this would be 4 to 3 but they say apples to bananas 3 2 4 3 apples for every 4 bananas

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Basic ratios (video) | Intro to ratios | Khan Academy

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Khan Academy (recipes)

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A ratio compares values.

A ratio says how much of one thing there is compared to another thing.

There are 3 blue squares to 1 yellow square

Ratios can be shown in different ways:

A ratio can be scaled up:

3 blue squares to 1 yellow square,
Here the ratio is also
even though there are more squares.

Try it Yourself

Using Ratios

The trick with ratios is to always multiply or divide the numbers by the same value.

Example:

4 : 5 is the same as 4×2 : 5×2 = 8 : 10

Recipes

Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.

So the ratio of flour to milk is 3 : 2

To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:

In other words, 12 cups of flour and 8 cups of milk.

The ratio is still the same, so the pancakes should be just as yummy.

"Part-to-Part" and "Part-to-Whole" Ratios

The examples so far have been "part-to-part" (comparing one part to another part).

But a ratio can also show a part compared to the whole lot.

Example: There are 5 pups, 2 are boys, and 3 are girls

Part-to-Part:

Part-to-Whole:

Try It Yourself

Scaling

We can use ratios to scale drawings up or down (by multiplying or dividing).

The height to width ratio of the Indian Flag is 2:3

So for every 2 (inches, meters, whatever) of height
there should be 3 of width.

If we made the flag 20 inches high, it should be 30 inches wide.

If we made the flag 40 cm high, it should be 60 cm wide (which is still in the ratio 2:3)

Example: To draw a horse at 1/10th normal size, multiply all sizes by 1/10th

This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is

1500 : 2000
What is that ratio when we draw it at 1/10th normal size?
We can make any reduction/enlargement we want that way.

Big Foot?

Allie measured her foot and it was 21cm long, and then she measured her Mother's foot, and it was 24cm long.

"I must have big feet, my foot is nearly as long as my Mom's!"
But then she thought to measure heights, and found she is 133cm tall, and her Mom is 152cm tall.

In a table this is:

The "foot-to-height" ratio in fraction style is:

We can simplify those fractions like this:

And we get this (please check that the calcs are correct):

"Oh!" she said, "the Ratios are the same".
"So my foot is only as big as it should be for my height, and is not really too big."
Practice

You can practice your ratio skills by Making Some Chocolate Crispies

1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 3603, 3604

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A ratio says how much of one thing there is compared to another thing. There are 3 blue squares to 1 yellow square Ratios can be shown in different ways: A ratio can be scaled up: 3 blue squares to 1 yellow square, Here the ratio is also even though there are more squares.

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- [VOICEOVER] Let's see if we can figure out what 4/3 minus 1/5 is, and if you think you know how to do it, I encourage you to pause the video and give it a go. So, when you first look at this, the thing that might jump out at you is we have different denominators here. So, it's not obvious how to subtract 1/5 from 4/3 when you have these different denominators and the key is, is to rewrite each of these fractions so that they have the same denominator. And how do we figure out what that same denominator is? Well, it's going to be a common multiple of three and five, and, ideally, it's going to be the least common multiple of three and five. So, how can we calculate that? Well, we can start with the larger of the two numbers, say five, and let's go through it's multiples and see when we get to one that's divisible perfectly by three. So, five is not divisible by three, 10 is not divisible by three, 15 is divisible by three. In fact, 15 is three times five. So, I can rewrite both of these fractions as something over 15. So, what's 4/3 if I were to rewrite it as something over 15? Well, to get from three to 15 in the denominator, we have to multiply by five. So, if you multiply the denominator by five, if you don't want to change the value of the fraction, you have to multiply the numerator by five as well. So, you have to multiply the numerator by five as well, four times five is going to be 20. So, 4/3 is the same thing as 20/15. Alright. Now, how would we rewrite 1/5 and something over 15? So, we're going to have 15 in the denominator. Well, to go from five to 15, we had to multiply by three. So, if we multiply the denominator by three, we have to multiply the numerator by three as well. So, times three. One times three is just three. So, 4/3 minus 1/5, we can rewrite that as 20/15 minus 3/15. Now, this becomes a lot more straight forward. What is this going to be? Well, this is going to be a certain number of fifteenths. We have 20/15 and we're taking away three of those fifteenths. So, we are going to have, if you have 20 of something and you take away three of them, you're going to have 17 of those things. In this case, we're talking about fifteenths. So, this is going to be 17/15. And if we wanted to write it as a mixed number, we could say 15 goes into 17 one time with a remainder of two. So, it's one and 2/15. Let's do another example. Let's see if we can figure out what 7/10 minus 5/8 is. Five over eight. And I encourage you to pause this video and see if you can calculate it yourself. Well, just like we saw before, we have different denominators but we need to rewrite them so they have a common denominator, that way, we can subtract. And so, what's a common multiple of 10 and eight and, ideally, the least common multiple. It doesn't have to be but it keeps things a little bit simpler. Well, let's start with the larger of the two numbers and then keep finding in their multiples and find one that is perfectly divisible by the other one, by eight. So, ten isn't perfectly divisible by eight, 20 isn't, 30 isn't, 40 is. 40 is a multiple of 10 and it's a multiple of eight. In fact, it's the least common multiple of 10 and eight. So, we can rewrite both of these fractions as something over 40. So, that's going to be something over 40 minus something over 40. Minus something over 40 is equal to something. So, 7/10 is what over 40? Well, to go from 10 to 40 in the denominator, we multiplied by four. So, we have to do the same thing in the numerator, multiply the numerator by four. Seven times four is 28. So, 7/10 is the same thing as 28/40. Now, let's do the same thing with the other fraction. To go from eight to 40 in the denominator, we had to multiply the denominator by five. Eight times five is 40. So, if we multiply the denominator by five, we have to multiply the numerator by five as well. Five times five is 25. So, 7/10 minus 5/8 is the exact same things as 28/40 minus 25/40 and now this makes a lot of sense. It's going to be a certain number of fortieths. If I have 28/40 and I take away 25 of those fortieths, how many fortieths am I going to have left? Well, I'm going to 3/40 left. 28/40 minus 25/40. So, I'm going to have 3/40. 28 minus 25 is three and we are done. 7/10 minus 5/8 is 3/40.

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Subtracting fractions with unlike denominators (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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You might like to read Adding Fractions first.

There are 3 simple steps to subtract fractions

Example 1:

Step 1. The bottom numbers are already the same. Go straight to step 2.

Step 2. Subtract the top numbers and put the answer over the same denominator:

Step 3. Simplify the fraction:

(If you are unsure of the last step see Equivalent Fractions.)

Example 2:

Step 1. The bottom numbers are different. See how the slices are different sizes? We need to make them the same before we can continue, because we can't subtract them like this:

To make the bottom numbers the same, multiply the top and bottom of the first fraction () by 3 like this:

× 3

× 3

And now our question looks like this:

−

The bottom numbers (the denominators) are the same, so we can go to step 2.

Step 2. Subtract the top numbers and put the answer over the same denominator:

In picture form it looks like this:

Step 3. Simplify the fraction:

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

Subtracting Mixed Fractions

I have a special page on Adding and Subtracting Mixed Fractions.

Making the Denominators the Same

In the previous example it was easy to make the denominators the same, but it can be harder ... so you may need to use either the

They both work, use which one you prefer!

Example: Cupcakes

You want to sell cupcakes at a market:

How much do you get?

First make the bottom numbers (the denominators) the same.

And multiply top and bottom of ¹/ ₄ by 5:

Now do the calculations:

Answer: you get to keep 3 20of total sales.

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You might like to read Adding Fractions first. Step 1. The bottom numbers are already the same. Go straight to step 2. Step 2. Subtract the top numbers and put the answer over the same denominator: Step 3. Simplify the fraction: (If you are unsure of the last step see Equivalent Fractions.)

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- [Voiceover] Let's say that we have the fraction 9/10, and I want to add to that the fraction 1/6. What is this, what is this going to equal? So when you first look at this, you say, "Oh, I have different denominators here. It's not obvious how I add these." And you'd be right and the way to actually move forward is to find a common denominator, to convert both of these fractions into fractions that have a common denominator. So how do you think about a common denominator? Well, a common denominator's gonna have to be a common multiple of these two denominators of 10 and six. So what's a common multiple of 10 and six? And it's usually simplest to find the least common multiple, and a good way of doing that is start with the larger denominator here, 10, and say, okay is 10 divisible by six? No. Okay, now, is 20 divisible by six? No. Is 30 divisible by six? Yes. 30 is divisible by six. So I'm just going through the multiples of 10 and saying, "Well what is the smallest multiple of 10 that is divisible by six?" And that's going to be 30. So I could rewrite both of these fractions as something over 30. So nine over 10. How would I write that as something over 30? Well I multiply the denominator, I'm multiplying the denominator by three. So I've just multiplied the denominator by three. So if I don't want to change the value of the fraction, I have to do the same thing to the numerator. I have to multiply that by three as well because now I'm just multiplying the numerator by three and the denominator by three, and that doesn't change the value of the fraction. So nine times three is 27. So once again, 9/10 and 27/30 represent the same number. I've just written it now with a denominator of 30, and that's useful because I can also write 1/6 with a denominator of 30. Let's do that. So 1/6 is what over 30? I encourage you to pause the video and try to think about it. So what did we do go from six to 30? We had to multiply by five. So if we multiply the denominator by five, we have to multiply the numerator by five as well, so one times five, one times five is five. So 9/10 is the same thing as 27/30, and 1/6 is the same thing as 5/30. And now we can add, now we can add and it's fairly straightforward. We have a certain number of 30ths, added to another number of 30ths, so 27/30 + 5/30, well that's going to be 27, that's going to be 27 plus five, plus five, plus 5/30, plus 5/30, which of course going to be equal to 32/30. 32 over 30, and if we want, we could try to reduce this fraction. We have a common factor of 32 and 30, they're both divisible by two. So if we divide the numerator and the denominator by two, numerator divided by two is 16, denominator divided by two is 15. So, this is the same thing as 16/15, and if I wanted to write this as a mixed number, 15 goes into 16 one time with a remainder one. So this is the same thing as 1 1/15. Let's do another example. Let's say that we wanted to add, we wanted to add 1/2 to to 11/12, to 11 over 12. And I encourage you to pause the video and see if you could work this out. Well like we saw before, we wanna find a common denominator. If these had the same denominator, we could just add them immediately, but we wanna find a common denominator because right now they're not the same. Well what we wanna find is a multiple, a common multiple of two and 12, and ideally we'll find the lowest common multiple of two and 12, and just like we did before, let's start with the larger of the two numbers, 12. Now we could just say well 12 times one is 12, so that we could view that as the lowest multiple of 12. And is that divisible by two? Yeah, sure. 12 is divisible by two. So 12 is actually the least common multiple of two and 12, so we could write both of these fractions as something over 12. So 1/2 is what over 12? Well to go from two to 12, you multiply by six, so we'll also multiply the numerator by six. Now we see 1/2, and 6/12, these are the same thing. One is half of two, six is half of 12. And how would we write 11/12 as something over 12? Well it's already written as something over 12, 11/12 already has 12 in the denominator, so we don't have to change that. 11/12, and now we're ready to add. So this is going to be equal to six, this is going to be equal to six plus 11, six plus 11 over 12. Over 12. We have 6/12 plus 11/12, it's gonna be six plus 11 over 12, which is equal to, six plus 11 is 17/12. If we wanted to write it as a mixed number, that is what, 12 goes into 17 one time with a remainder of five, so 1 5/12. Let's do one more of these. This is strangely fun. Alright. Let's say that we wanted to add, We're gonna add 3/4 to, we're gonna add 3/4 to 1/5. To one over five. What is this going to be? And once again, pause the video and see if you could work it out. Well we have different denominators here, and we wanna find, we wanna rewrite these so they have the same denominators, so we have to find a common multiple, ideally the least common multiple. So what's the least common multiple of four and five? Well let's start with the larger number, and let's look at its multiples and keep increasing them until we get one that's divisible by four. So five is not divisible by four. 10 is not divisible by four, or perfectly divisible by four is what we care about. 15 is not perfectly divisible by four. 20 is divisible by four, in fact, that is five times four. That is 20. So what we could do is, we could write both of these fractions as having 20 in the denominator, or 20 as the denominator. So we could write 3/4 is something over 20. So to go from four to 20 in the denominator, we multiplied by five. So we also do that to the numerator. We multiply by three times five to get 15. All I did to go from four to 20, multiplied by five. So I have to do the same thing to the numerator, three times five is 15. 3/4 is the same thing as 15/20, and over here. 1/5. What is that over 20? Well to go from five to 20, you have to multiply by four. So we have to do the same thing to the numerator. I have to multiply this numerator times four to get 4/20. So now I've rewritten this instead of 3/4 plus 1/5, it's now written as 15/20 plus 4/20. And what is that going to be? Well that's going to be 15 plus four is 19/20. 19/20, and we're done.

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Adding fractions with unlike denominators (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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A fraction like says we have 3 out of the 4 parts the whole is divided into.

To add fractions there are Three Simple Steps:

Step 1: Make sure the bottom numbers (the denominators) are the same

Step 2: Add the top numbers (the numerators), put that answer over the denominator

Step 3: Simplify the fraction (if possible)

Example:

Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2. Add the top numbers and put the answer over the same denominator:

Step 3. Simplify the fraction:

In picture form it looks like this:

Example:

Step 1: The bottom numbers are different. See how the slices are different sizes?

We need to make them the same before we can continue, because we can't add them like that.

The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the top and bottom of the first fraction by 2, like this:

× 2

× 2

Important: you multiply both top and bottom by the same amount,
to keep the value of the fraction the same

Now the fractions have the same bottom number ("6"), and our question looks like this:

The bottom numbers are now the same, so we can go to step 2.

Step 2: Add the top numbers and put them over the same denominator:

In picture form it looks like this:

Step 3: Simplify the fraction:

In picture form the whole answer looks like this:

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

A Rhyme To Help You Remember
♫ "If adding or subtracting is your aim,
The bottom numbers must be the same!
♫ "Change the bottom using multiply or divide,
But the same to the top must be applied,
♫ "And don't forget to simplify,
Before its time to say good bye"
Example:

Again, the bottom numbers are different (the slices are different sizes)!

But let us try dividing them into smaller sizes that will each be the same:

The first fraction: by multiplying the top and bottom by 5 we ended up with :

× 5

× 5

The second fraction: by multiplying the top and bottom by 3 we ended up with :

× 3

× 3

The bottom numbers are now the same, so we can go ahead and add the top numbers:

The result is already as simple as it can be, so that is the answer:

Making the Denominators the Same

In the previous example how did we know to cut them into ths to make the denominators the same? We simply multiplied the two denominators together (3 × 5 = 15).

Read about the two main ways to make the denominators the same here:

They both work, use which one you prefer!

Example: Cupcakes

You want to make and sell cupcakes:

A friend can supply the ingredients, if you give them ¹/₃ of sales

And a market stall costs ¹/₄ of sales

How much is that altogether?

First make the bottom numbers (the denominators) the same.

And multiply top and bottom of ¹/ ₄ by 3:

Now do the calculations:

Answer: of sales go in ingredients and market costs.

Adding Mixed Fractions

We have a special (more advanced) page on Adding Mixed Fractions.

930,931, 1399,932, 1400,933, 1401, 1402, 3564, 3565

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To add fractions there are Three Simple Steps: Step 1: Make sure the bottom numbers (the denominators) are the same, Step 2: Add the numerators, put that answer over the denominator, Step 3: Simplify the fraction (if needed)

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Multiplying and Dividing Fractions - BrainPOP

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Tim and Moby show you how to multiply and divide fractions in this BrainPOP movie! Dividing can actually make a number bigger?!

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This interactive activity explores the representation of fractions, decimals and percentages using either a square or circle divided into equal parts. When the activity is launched, a 100 square grid is shown. Click the random button to create a grid of different colors. The squares change so they are either orange or white. You can change the number of colors using the color number control, change it to 5 and press random again and there will now be 5 different colors in the grid. You can arrange the grid automatically by clicking arrange button, to reset the grid back to white click the trash button

To select your own fraction simply select one of the colors and click and drag your mouse over the either the grid or the circle.

Display options

The initial set up is ideal for explaining percentages since there are 100 squares, but this can be changed by using the divisions selection. You can also change from the square to a circle by clicking the shape toggle control

Hiding or Showing the values

On the right side of the screen our colored rectangles with ? labels. Click one of these to turn the rectangle over to display its decimal,percentage or fraction value. To change a whole column click one of the above to toggle hide or show. Note values on display automatically change as the grid or circle is changed.

The fraction values by default are simplified, to change this click the cancel fraction toggle control.

Related activities

This activity is closely related to the interactive fraction wall. Ihe interactive clock can also be used to display fractions using a clock face.

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fraction as a decimal | fraction simplifier | fraction circle | fraction square

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Fraction as a decimal, teaching resource, show a fraction pie or square. Corresponding values as fractions decimals or percentages. Visnos interactive teaching resource.

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- [Voiceover] What I want to explore in this video is the notion of a "rate." So, let's look at some examples of rates that you've probably encountered in your everyday life. So, if you're driving in your car down the road, and you're looking at the speedometer, you might see that it says that you are going 35 M-P-H, where the M-P-H stands for 35 miles per, per hour. Well, what's that saying? That's saying, well, every hour, how many miles are you going if you were to stay at that current rate. So, it could be a measure of speed. How much distance are you covering per unit time? And, most typically, when people talk about rates, that's what they're talking about. They're talking about how much of something that is happening per unit time. And, it doesn't have to be even distance per unit time, you might have a, you might have your hourly rate for someone who is doing some type of a job. They might say that they're making, they're making $10, so they're making $10. And, actually, let me write the dollars out so the units become a little bit more obvious, 10 dollars, dollars per hour, dollars per, dollars per hour. And so, once again, this is how much money. It's not talking about distance anymore. How much money is being earned per unit time? And, so, even though rates are often associated with how much something is happening per some unit time, and it could be miles per hour, or it could be meters per second, or, in this case, it could be a wage, it could be dollars per hour. Rates don't have to be just in those terms. In fact, you might say, "All right, "I have a dessert that I really enjoy, "but I'm very conscientious "about, about the number of calories that I consume." And, you might, you might see something like, there are 200 calories, calories per serving, per serving. And, so, this is telling us the number of calories per a serving. And they'll tell us what a serving is. A serving might be a cup or eight ounces or whatever else. And, so, I could say, "Okay, look, if I have two servings, "then I'm gonna have 400 calories. "Same way, if I work two hours, I'm gonna have 20 dollars. "If I, or if I go two hours, "I'm gonna go 70 miles." So, rates give you a sense. It's like, how fast is something happening? Or how much of one thing is happening for every time something else happens? Now, I can write rates so they look an awful lot like a ratio. And, these words are, actually, very related, 'cause you see that even how they're written. R-A-T, R-A-T. Their roots are coming from the exact same idea. In fact, this rate over here, 35 miles per hour, it could come from, "Hey, I just, I just went 35 miles in one hour, "what's the ratio?" So, the ratio of miles to hours. And, then, you could say, "Well, I went 35, "the ratio miles to hours "was 35 to one." Or it could have been, maybe it was 70 to two or something like that. But, that could have been reduced to 35 to one. So, as a ratio, you would typically see it written like this... Or maybe see it written like, see it written like this... And, sometimes, you might even see it written like this, 35 miles to one hour. But, now it's starting to resemble more of the special case of a ratio, which we call a "rate." Because, this is the same thing as 35. Instead of writing it out "miles per hour," you'll often see it written like this, miles per, miles per hour. So, these are very, very related ideas. If you find the ratio between calories and servings, well, then, you're going to be able to write, you're going to be able to express it as a rate and vice versa. Now, why do we care about rates? Well, especially if we're thinking about things like speed, without rates, it would be hard to quantify how fast things are happening. Otherwise, we'd be in a world where we're saying, "Hey, I'm faster than you," or "She's faster than me." But we wouldn't be able to quantify exactly how fast they are. But with rates, we can say, "Hey, that person ran "a hundred meters in 10 seconds, "they run 10 meters per second." We can quantify exactly how fast that thing is happening, the rate at which it is happening. Here, instead of saying, "Hey, a cup of that "is gonna give you, is gonna give you more energy, or, maybe, contribute more to your weight than a cup of that, and making these relative comparisons, here, you can actually, you can actually quantify things. And when we study rate, we're gonna study rate a lot in mathematics. It's gonna be essential in algebra when we look at the rate of change of a line, how far it moves in the vertical direction relative to the horizontal direction. We're gonna call that "slope". And you can even imagine the slope of a hill as how fast is it climbing for as much as you move forward. But we're also gonna study rates in detail when we go to calculus. In fact, the whole basis of differential calculus, that you might see later in high school and early college, is all about measuring instantaneous rate. How fast is something going right now? So, rates are really, really interesting, really, really important. And, I would guess that, if you just look around your life, even over the next few hours, you're going to encounter many, many, many rates.

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Voiceover] What I want to explore in this video is the notion of a "rate." So, let's look at some examples of rates that you've probably encountered in your everyday life. So, if you're driving in your car down the road, and you're looking at the speedometer, you might see that it says that you are going 35 M-P-H, where the M-P-H stands for 35 miles per, per hour.

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Voiceover:We've got some apples here and we've got some oranges and what I want to think about is, what is the ratio, what is the ratio of apples ... Of apples, to oranges? To oranges. To clarify what we're even talking about, a ratio is giving us the relationship between quantities of 2 different things. So there's a couple of ways that we can specify this. We can literally count the number of apples. 1, 2, 3, 4, 5, 6. So we have 6 apples. And we can say the ratio is going to be 6 to, 6 to ... And then how many oranges do we have? 1, 2, 3, 4, 5, 6, 7, 8, 9. It is 6 to 9. The ratio of apples to oranges is 6 to 9. And you could use a different notation. You could also write it this way. 6 to ... You would still read the ratio as being 6 to 9. But we don't have to just satisfy us with this because one way to think about ratios, especially if we're thinking about apples to oranges, is how many apples do we have for a certain number of oranges? When you think about it that way, we can actually reduce these numbers, as you might have already thought about. Both 6 and 9 are divisible by 3. So just like we can reduce fractions, we can also reduce ratios. So if you divide 6 and 9 both by 3. 6 divided by 3 is 2. 6 divided by 3 is 2. And 9 divided by 3 is 3. So we could also say that the ratio of apples to oranges is 2 to 3. Or if we want to use this notation, 2 to 3. 2 to 3. Now, does that make sense? Well look. We divided each of these groups into 3. So one way to think about it ... If you divide this whole total into 3 groups. So 1 group, 1 group. 2 groups, 2 groups. And 3 equal groups. We see that in each of those groups, for every 2 apples, for every 2 apples, we have 3 oranges. For 2 apples we have 3 oranges. For 2 apples we have 3 oranges. So, once again, the ratio of apples to oranges. For every 2 apples we have 3 oranges. But we could think about things the other way around as well. We could also think about what is the ratio ... We could also think about what is the ratio ... Ratio, of oranges to apples? Oranges to apples. And here we would, essentially, switch the numbers. The ratio of oranges to apples. Notice, up here we said apples to oranges which is 6 to 9 or 2 to 3 if we reduce them. And here we're going to say the ratio of oranges to apples, so we've swapped these 2. So we're going to swap the numbers. Here we have 9 oranges for every 6 apples. So we could say the ratio is going to be 9 to 6. The ratio is 9 to 6. Or if we want to reduce it, for every 3 oranges ... So we're going to divide this by 3. So for every 3 oranges we are going to have 2 apples. We are going to have 2 apples. So notice, this is just exactly what we had up here, but when we had apples to oranges it was 6 to 9. 6 apples for every 9 oranges. And now when it's oranges to apples, we say it's 9 to 6. 9 oranges for every 6 apples. Or we could say for every 3 oranges we have exactly 2 apples.

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Voiceover:We've got some apples here and we've got some oranges and what I want to think about is, what is the ratio, what is the ratio of apples ... Of apples, to oranges? To oranges. To clarify what we're even talking about, a ratio is giving us the relationship between quantities of 2 different things.

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Write 18% as a decimal and as a fraction in simplest form. So let's do it as a decimal first. So 18% is the same thing as 18 per 100, or 18 per cent. I'm actually separating out the percent, it's only going to be one word, but I'm writing it as, literally, per cent. Cent means the same thing as 100. So this literally means 18 per 100. Actually, I said I would do the decimal first, but we can start putting it into a fraction first. 18 per 100 as a fraction literally means 18/100. We're literally doing the fraction first. This literally means 18 per 100, or 18 hundredths. From here we can go straight to a decimal or we could do this fraction in simplest form. Let's do the decimal first, just because that's actually what I said I would do first. Let's do that first. This is the same thing as 18 hundredths. And we know how to write that in decimal form. It's 0.18. You could view this as 1 tenth and 8 hundredths, which is the same thing, or 10 hundredths and 8 hundredths, which is 18 hundredths. So this is written in decimal form. And if we write it as a simplified fraction, we need to see if there is a common factor for 18 and 100. And they're both even numbers, so we know they're both divisible by 2, so let's divide both the numerator and the denominator by 2. So we have 18 divided by 2 over 100 divided by 2. And we're going to get 18 divided by 2 is 9. 100 divided by 2 is 50. And I don't think these guys share any common factors. 50 is not divisible by 3. 9 is only divisible by 3 and 1 and 9. So this is the fraction in simplest form. So we have 18% is the same thing as 0.18, which is the same thing, in simplest form, as 9/50. Now, I went through a lot of pain here to show you that this really just comes from the word, from percent, from per 100. But if you ever were to see this in a problem, the fast way to do this is to immediately say, OK, if I have 18%, you should immediately say, anything in front of the percent-- that's that anything, whatever this anything is-- it should be equal to that anything. In this case it's 18/100. And another way to think about it, you could view this as 18.0%. I just added a trailing zero there, just so that you see the decimal, really. But if you want to express this as a decimal without the percent, you just move the decimal to the left two spaces. So if we move the decimal to the left two spaces, one, two, this becomes 0.18. Or you could immediately say that 18% as a fraction is 18/100. When you put it in simplified form, it's 9/50. But you should also see that 18/100, and we have seen this, is the exact same thing as 18 hundredths, or 0.18. Hopefully, this made some connections for you and didn't confuse you.

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Converting percents to decimals & fractions example (video) | Khan Academy

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Write 18% as a decimal and as a fraction in simplest form. So let's do it as a decimal first. So 18% is the same thing as 18 per 100, or 18 per cent. I'm actually separating out the percent, it's only going to be one word, but I'm writing it as, literally, per cent.

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Finding common denominators of multiple fractions to order them

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Comparing improper fractions and mixed numbers

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Worked examples comparing improper fractions and mixed numbers

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Write 7/4 as a mixed number. So right now it's an improper fraction. 7 is larger than 4. Let's write it is a mixed number. So first I'm just going to show you a fairly straightforward way of doing it and then we're going to think a little bit about what it actually means. So to figure out what 7/4 represents as a mixed number, let me write it in different colors. So this is going to be equal to-- the easiest way I do it is you say, well, you divide 4 it 7. If we're dealing with fourths, 4 goes into 7 a total of one time. Let me do this in another color. 1 times 4 is 4. And then what is our remainder? 7 minus 4 is 3. So if we wanted to write this in plain-- well, let me just do the problem, and then we'll think about what it means in a second. So you see that 4 goes into 7 one time, so you have one whole here, and then how much do you have left over? Well, you have 3 left over, and that comes from right over there. That is the remainder when you divide 4 into 7. 3 left over, but it's 3 of your 4, or 3/4 left over. So that's the way we just converted it from an improper fraction to a mixed number. Now, it might seem a little bit like voodoo what I just did. I divided 4 into 7, it goes one time, and then the remainder is 3, so I got 1 and 3/4. But why does that make sense? Why does that actually makes sense? So let's draw fourths. Let's draw literally 7 fourths and maybe it'll become clear. So let's do a little square as a fourth. So let's say I have a square like that, and that is 1/4. Now, let's think about what seven of those mean, so let me copy and paste that. Copy and then paste it. So here I have 2 one-fourths, or you could see I have 2/4. Now I have 3 one-fourths. Now, I have 4 one-fourths. Now this is a whole, right? I have 4 one-fourths. This is a whole. So let me start on another whole. So now I have 5. Now I have 6 one-fourths, and now I have 7 one-fourths. Now, what does this look like? So all I did is I rewrote 7/4, or 7 one-fourths. I just kind of drew it for you. Now, what does this represent? Well, I have 4 fourths here, so this is 4/4. This right here is 3/4. Notice, 7/4 is 4/4 with 3/4 left over. So let me write it this way. 7/4 is 4/4 with 3/4 left over. Now what is 4/4? 4/4 is one whole. So you have one whole with 3/4 left over, so you end up with 1 and 3/4. So that is the 3/4 part and that is your one whole. Hopefully that makes sense and hopefully you understand why it connects. Because you say, well, how many wholes do you have? When you're dividing the 4 into the 7 and getting the one, you're essentially saying how many wholes? So the number of wholes, or you can imagine, the number of whole pies. And then how many pieces do we have left over? Well, we have 3 pieces and each piece is 1/4, so we have 3/4 left over. So we have one whole pie and three pieces, which are each a fourth left over.

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Writing improper fractions as mixed numbers (video) | Khan Academy

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Write 7/4 as a mixed number. So right now it's an improper fraction. 7 is larger than 4. Let's write it is a mixed number. So first I'm just going to show you a fairly straightforward way of doing it and then we're going to think a little bit about what it actually means.

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Interactivate: Fraction Four

Fraction Four: Students play a generalized version of connect four, gaining the chance to place a piece after simplifying fractions, converting fractions to decimals and percentages, and answering algebra questions involving fractions. Choose difficulty level, question types, and time. Fraction Four is one of the Interactivate assessment games.

On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment, faculty enhancement, and interactive curriculum development at all levels. Student development of numerical models and simulations integrated with core curriculum provides an opportunity to gain practical experience in computational science. Additionally, the National Computational Science Institute (NCSI) provides nation-wide workshops portraying resources and instructional ideas to middle school, high school, and undergraduate instructors for use in the classroom. Resources and materials offered to these instructors are available free of charge from Shodor's website and are largely developed by Shodor student interns. Shodor's academic program efficiently guides participants from excitement to experience to expertise through computational explorations, research opportunities, and service.

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Interactivate: Fraction Four On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment, faculty enhancement, and interactive curriculum development at all levels. Student development of numerical models and simulations integrated with core curriculum provides an opportunity to gain practical experience in computational science.

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Have fun playing this interactive online Simplifying Fractions Soccer Game. Solve the math problem and get a chance to kick the soccer ball to try to give your "team" a goal.

In this game students will discover that numbers can be written as the sums and differences of other numbers. The game can be played alone, in pairs, or in teams. This game can be played on computers, iPads, and other tablets. You do not need to install an app to play this game on the iPad.

The game is based on the following Common Core Math Standard:

CCSS.Math.Content.3.NF.A.3
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

CCSS.Math.Content.3.NF.A.3.a
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

CCSS.Math.Content.3.NF.A.3.b
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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Have fun playing this interactive online Simplifying Fractions Soccer Game. Solve the math problem and get a chance to kick the soccer ball to try to give your "team" a goal. In this game students will discover that numbers can be written as the sums and differences of other numbers.

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Matching Fractions Level 4. Fun free flash games teach logical thinking and math skills.

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A visual aid for a teacher to use in a Mathematics lesson

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I say! Did you know a fraction can be improper? Tim and Moby teach you all about mixed numbers.

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Would you prefer two-twelfths or three-eighteenths of a pizza? It's the same amount either way you slice it. Learn why!

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A fraction is a part of a whole

You can learn about:

Fractions

Introduction to Fractions

Decimals, Fractions and Percentages

Interactive Fractions

Fractions on a pizza and the number line

Decimals, Fractions and Percentages on the Number Line

Words to Pizza

Words to Number Line

Fraction to Pizza

Fraction to Number Line

Fractions on a Clock Face

The three different types of fractions

Proper Fractions

Improper Fractions

Mixed Fractions

How to simplify a fraction, and how the "Greatest Common Factor" can help

Equivalent Fractions

Fraction Number Line

Simplifying Fractions

Greatest Common Factor

Greatest Common Factor Tool

How to compare fractions, and how the "Least Common Multiple" can help

Comparing Fractions

Least Common Multiple

Least Common Multiple Tool

Least Common Denominator

How to add, subtract, multiply and divide fractions

♫ "Multiplying fractions no big problem,
Top times top over bottom times bottom,

"Dividing fractions, easy as pie,
Flip the second fraction, then multiply,

"If adding or subtracting is your aim,
The bottom numbers must be the same!

"Change the bottom using multiply or divide,
But the same to the top must be applied,

"And don't forget to simplify,
Before it's time to say goodbye"  ♫

Multiplying Fractions

Dividing Fractions

Adding Fractions Adding Fractions Illustrated

Subtracting Fractions Subtracting Fractions Illustrated

Dividing Fractions by Whole Numbers

Adding Mixed Fractions

Multiplying Mixed Fractions

How to convert fractions to decimals and vice versa

Convert Decimals to Fractions and Decimal to Fraction Converter

Converting Fractions to Decimals

How to convert fractions to percentages and vice versa

Convert Percentages to Fractions

Converting Fractions to Percentages

Reciprocal fractions

Reciprocal Fractions

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1) Represent, compare, and order fractions (improper fractions and mixed numbers)

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1) Represent, compare, and order fractions (improper fractions and mixed numbers)