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Here are the 3 ways you can write a ratio.

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Here are the 3 ways you can write a ratio.

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The Ratio and Fraction song, Stereo Hearts Remix

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Work through this HyperDoc about ratios!

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Difference between ratios and proportions

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Difference between ratios and proportions

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Ratio and proportion are two mathematical concepts which have end number of practical applications in different spheres of life. The ratio is used to compare the quantities of two different categories like the ratio of men to women in the city. Here, men and women are the two different categories.

On the contrary, Proportion is used to find out the quantity of one category over the total, like the proportion of men out of total people living in the city.

Ratio defines the quantitative relation between two amounts, representing the number of time one value contains the other. Conversely, Proportion is that part that that explains the comparative relation with the entire part. This article presents you the basic differences between ratio and proportion. Have a look.

Content: Ratio Vs Proportion

Comparison Chart

Meaning

Ratio refers to the comparison of two values of the same unit.

When two ratios are set equal to each other, it is called as proportion.

Denoted by

Colon (:) sign

Double Colon (::) or Equal to (=) sign

Represents

Quantitative relationship between two categories.

Quantitative relationship of a category and the total

Definition of Ratio

In mathematics, the ratio is described as the comparison of the size of two quantities of the same unit, which is expressed in terms of times i.e. the number of times the first value contains the second. It is expressed in its simplest form. The two quantities under comparison are called the terms of ratio, where the first term is antecedent and the second term is consequent.

For example: In the given figure, there are 3 red flower to 2 blue flowers, i.e. 3 : 2. So 3 and 2 are two quantities of the same unit, the fraction of these two quantities (3/2) is known as its ratio. Here, 3 & 2 are the terms of the ratio, where 3 is antecedent while 2 is consequent.

There are few points to remember in relation to ratio, which is mentioned as under:

Both antecedent and consequent can be multiplied by the same number. The number should be non-zero.

The order of the terms is significant.

The existence of ratio is only between the quantities of the same kind.

The unit of the quantities under comparison should also be same.

Comparison of two ratios can only be done if they are in equivalent like the fraction.

Definition of Proportion

Proportion is a mathematical concept, which states the equality of two ratios or fractions. It refers to some a category over the total. When two sets of numbers, increase or decrease in the same ratio, they are said to be directly proportional to each other.

For example, 1 out of 3 flowers is red = 2 out of 6 flowers is red.

Four numbers p, q, r, s are considered to be in proportion if p : q = r : s, then p/q = r/s, i.e. ps = qr (by cross multiplication rule). Here p, q, r, s are called the terms of proportion, wherein p is the first term, q is the second term, r is the third term, and s is the fourth term. The first and fourth term are called extremes while the second and third term are called means i.e. middle term. Further, if there are three quantities in continuous proportion, then the second quantity is the mean proportion between the first and third quantity.

Important properties of proportion are discussed below:

Invertendo - If p : q = r : s, then q : p = s : r

Alternendo - If p : q = r : s, then p : r = q : s

Componendo - If p : q = r : s, then p + q : q = r + s : s

Dividendo - If p : q = r : s, then p - q : q = r - s : s

Componendo and dividendo - If p : q = r : s, then p + q : p - q = r + s : r - s

Addendo - If p : q = r : s, then p + r : q + s

Subtrahendo - If p : q = r : s, then p - r : q - s

Key Differences Between Ratio and Proportion

The difference between ratio and proportion can be drawn clearly on the following grounds:

1. Ratio is defined as the comparison of sizes of two quantities of the same unit. Proportion, on the other hand, refers to the equality of two ratios.

2. The ratio is an expression while proportion is an equation which can be solved.

3. The ratio is represented by Colon (:) sign between the quantities compared. In contrast proportion, is denoted by Double Colon (::) or Equal to (=) sign, between the ratios under comparison.

4. The ratio represents the quantitative relationship between two categories. As opposed to proportion, which shows the quantitative relationship of a category with the total.

5. In a given problem, you can identify whether they are in ratio or proportion, with the help of keywords they use i.e. 'to every' in ratio and 'out of' in the case of proportion.

Example

There are total 80 students in class, out of which 30 are boys and rest of the students are girls. Now find out the following:
(i) Ratio of boys to girls and girls to boys
(ii) Proportion of boys and girls in the class

Solution: (i) Ratio of boys to girls = Boys:Girls = 30:50 or 3 : 5
Ratio of girls to boys = Girls: Boys = 50 : 30 or 5 : 3
Thus, For every three boys there are five girls or for every five girls, there are three boys.

(ii) Proportion of boys = 30/80 or 3/8
Proportion of girls = 50/80 or 5/8
Thus, 3 in every 8 students is a boy and 5 in every 8 students is a girl.

Conclusion

Therefore, with the above discussion and examples, one can easily understand the differences between these two mathematical concepts. The ratio is the comparison of two numbers while proportion is nothing but an extension over ratio which states that two ratios or fraction are equivalent.

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Difference Between Ratio and Proportion (with Comparison Chart) - Key Differences

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Ratio and proportion are two mathematical concepts which have end number of practical applications in different spheres of life. The ratio is used to compare the quantities of two different categories like the ratio of men to women in the city. Here, men and women are the two different categories.

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Work through this lesson on Khan Academy to learn and get skilled on working with ratios!

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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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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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Here are ways that ratios are used in real-world situations.

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How to Use Ratios & Proportions in Real Life

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Two special ratios consistently seen in real life are pi (3.14) and phi (1.618). Pi is the relationship between the circumference of a circle and its diameter. In the real world, pi can be used to calculate the circumference of a circular swimming pool, provided you know the diameter or radius.

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grade 6  free math games practice common core standards