Dividing Fractions
If your friend has half a pie, how many quarter-pies are in that half? Or, to put this into mathematical notation:
1/2 ÷ 1/4 = ?
To get the answer, flip the divisor (the second fraction) over, and then multiply the fractions. (Or, to put it another way, multiply the dividend [the first fraction] by the reciprocal of the divisor [the second fraction].)
In this case, that makes the problem:
1/2 x 4/1 = ?
We begin by multiplying the numerators:
1 x 4 = 4
And then we multiply the denominators:
2 x 1 = 2
The answer has a numerator of 4 and a denominator of 2. In other words:
1 x 4/2 x 1 =4/2
This fraction can be reduced to lowest terms:
4 ÷ 2/2 ÷ 2 =2/1 = 2
There are 2 quarter-pies in a half-pie.
Another Example
Let's try another:
4/5 ÷ 6/7 = ?
We flip the divisor over, and change the division sign to a multiplication sign:
4/5 x 7/6 = ?
We multiply the numerators:
4 x 7 = 28
And we multiply the denominators:
5 x 6 = 30
The answer has a numerator of 28 and a denominator of 30. In other words:
4 x 7/5 x 6 =28/30
We can reduce this fraction by dividing the numerator and denominator by 2:
28 ÷ 2/30 ÷ 2 = 14/15
Mixed Numbers
Let's try one more, this time with a mixed number:
21/4 ÷ 2/3 = ?
First we change the mixed number to an improper fraction:
9/4 ÷ 2/3 = ?
Next we flip the divisor over and change the division sign to a multiplication sign:
9/4 x 3/2 = ?
We multiply the numerators:
9 x 3 = 27
And we multiply the denominators:
4 x 2 = 8
The answer has a numerator of 27 and a denominator of 8. In other words:
9 x 3/4 x 2 =27/8
Finally, we turn the result—an improper fraction—into a mixed number.
27/8 = 33/8 =