Dividing Rational Numbers

Pre-Algebra

Vocabulary

Rational Number: Any number that can be written as a fraction.

Reciprocal/Multiplicative Inverse:Two numbers whose product is 1.(Switch the numerator and the

denominator.)

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5

24÷15

36Example:

In order to divide fractions, just remember Kentucky Chicken Fried.K – Keep the first fraction the sameC – Change the division to multiplicationF – Flip the second fraction (take the reciprocal)

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5

24

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•

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36

15

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5

24÷15

36

We keep the first fraction in our problem.We change the division to multiplication.We flip the second fraction by taking the reciprocal .

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5

24•36

15

Now we multiply.

Since 5 and 15 share a factor of 5, we may factor out 5 from our problem.€

1

€

3

Since 24 and 36 share a factor of 12, we may factor out 12 from our problem.

We multiply across horizontally.

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2

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3

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=

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3

6

Finally, we simplify if necessary.

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=

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1

2

Example #2:

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−21

3÷ 54

9This time we must change our mixed numbers into improper fractions!

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−21

3

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×

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+ First we multiply 3 and 2 which yields 6.

Then we add 1 to 6 and get 7.

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54

9

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×

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+ First we multiply 9 and 5 which yields 45.

Then we add 4 to 45 and get 49.

Our new problem is now:

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−73÷49

9We now use Keep, Change, Flip (KCF) to divide.

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−73

K

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•

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9

49

C F

We factor.

And finally, we multiply.€

−1

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1

€

7

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3

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=

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−37