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.)
€
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)
€
5
24
€
•
€
36
15
€
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 .
€
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.
€
2
€
3
€
=
€
3
6
Finally, we simplify if necessary.
€
=
€
1
2
Example #2:
€
−21
3÷ 54
9This time we must change our mixed numbers into improper fractions!
€
−21
3
€
×
€
+ First we multiply 3 and 2 which yields 6.
Then we add 1 to 6 and get 7.
€
54
9
€
×
€
+ First we multiply 9 and 5 which yields 45.
Then we add 4 to 45 and get 49.
Our new problem is now:
€
−73÷49
9We now use Keep, Change, Flip (KCF) to divide.
€
−73
K
€
•
€
9
49
C F
We factor.
And finally, we multiply.€
−1
€
1
€
7
€
3
€
=
€
−37
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