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Quizlet- practice ordering rational numbers

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Quizlet- practice ordering rational numbers

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A set of more difficult problems comparing fractions to fractions, fractions to decimals, and decimals to decimals. Look at the terms provided and order th...

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Khan Academy- review of Ordering Numbers

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Khan Academy- review of Ordering Numbers

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Video transcript

I've got five numbers here, and the goal is to order them from least to greatest. And it might be obvious to you that all five of these numbers are negative numbers. So let's just think about which of these is the greatest number. And you might be tempted to say oh, well, you know, if these were all positive, 40 would be the greatest. So you might be tempted to say negative 40 is the greatest. But you have to realize what the negative is telling you, and to think about that. Think about if these were your dollar amounts in your bank account. Would you rather have negative $40 in your bank account or negative $7 in your bank account? Negative 40 means that you owe the bank $40. So it's 40 less than having nothing. Negative 7 would mean that you owe the bank only $7. So it's actually the case that negative 40 is less than negative 7. And out of all of these numbers, it is the least of all of them. So negative 40 is the very least that you could do. That's the least amount of money that you would want out of these comparisons in your bank account, or the smallest amount of money. You owe the bank $40. Not only do you have nothing, you owe the bank $40. Then the next smallest number would be negative 30. And then the next smallest after that would be negative 25. And then the next smallest after that would be negative 10. And then finally, the greatest of all of these numbers-- and I will do it in pink-- the greatest of all of these numbers is negative 7. And if it's still not obvious to you, you could also think of them in temperature terms. Which of these is the coldest temperature, whether you're talking about Celsius or Fahrenheit? Negative 40 would be the coldest temperature. Negative 7 would be the warmest temperature. There would be the most heat in the air at negative 7. Another way to think about it is we could draw a number line. So let's draw a number line right over here. If this is a zero, and we could put maybe positive 7 up here. Positive 7 isn't one of these numbers, but then we could plot all the other numbers. So this right here might be negative 7. If that's negative 7, then maybe this right over here would be negative 10. Notice we go further and further to the left of zero. And then we go a little bit further to the left. We get negative 25. A little bit further to the left than that is negative 30. And then you go even further to the left and you get to negative 40. So if you think of it this way, the least of these numbers is the one that's furthest to the left on the number line, and the greatest is the one that's furthest to the right.

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Ordering negative numbers (video) | Khan Academy

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How to add, subtract, multiply and divide rational numbers

A rational number is a number that can be written as a simple fraction (i.e. as a ratio).

Examples:

So a rational number looks like this:

But q cannot be zero, as that is dividing by zero.

How to Add, Subtract, Multiply and Divide

When the rational number is something simple like 3, or 0.001, then just use mental arithmetic, or a calculator!
But what about when it is in p q form? Here we will see those operations in a more general Algebra style.
You might also like to read Fractions in Algebra.

Let us start with multiplication, as that is the easiest.

Multiplication

To multiply two rational numbers multiply the tops and bottoms separately, like this:

Here is an example:

Division

To divide two rational numbers, first flip the second number over (make it a reciprocal) and then do a multiply like above:

Here is an example:

Addition and Subtraction

We will cover Addition and Subtraction in one go, as they are the same method.

Before we add or subtract, the rational numbers should have the same bottom number (called a Common Denominator).

The easiest way to do this is to

Multiply both parts of each number by the bottom part of the other

Like this (note that the dot · means multiply):

Here is an example of addition:

And an example of subtraction (the middle step is skipped to make it quicker):

Simplest Form

Sometimes we have a rational number like this:

But that is not as simple as it can be!

We can divide both top and bottom by 5 to get:

÷ 5

10 2 3 15 =

÷ 5

Now it is in "simplest form", which is how most people want it!

Be Careful With "Mixed Fractions"

We may be tempted to write an Improper Fraction (a fraction that is "top-heavy", i.e. where the top number is bigger then the bottom number) as a Mixed Fraction:

Improper Fraction

Mixed Fraction

⁷/ ₄

1 ³/ ₄

=

But for mathematics the "Improper" form (such as ) is actually better.

Because Mixed fractions (such as 1 ) can be confusing when we write them down in a formula, as it can look like a multiplication:

Mixed Fraction:

What is:

1 + 2 1 4 ?

Is it:

1 + 2 + 1 4 = 3 1 4 ?

Or is it:

1 + 2 × 1 4 = 1 1 2 ?

Improper Fraction:

What is:

1 + 9 4 ?

It is:

4 9 13 4 4 = 4 +

So try to use the Improper Fraction when doing mathematics.

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How to add, subtract, multiply and divide rational numbers A rational number is a number that can be written as a simple fraction (i.e. as a ratio). So a rational number looks like this: But q cannot be zero, as that is dividing by zero.

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Explanation of textbook examples

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Don't forget!

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Multiplying and Dividing Rational Numbers Video

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Multiplying and Dividing Rational Numbers Video

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Multiplying and Dividing Rational Numbers

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Explanation of textbook examples