secrets-of-mental-math-malestrom

Dividing Fractions
Dividing fractions is just as easy as multiplying fractions.
There’s just one extra step. First, turn the second fraction upside
down (this is called the reciprocal) then multiply. For instance,
the reciprocal of 4 5 is 5 4 . Therefore,
Divide and Conquer: Mental Division 103
2 4 2 5 10
3 5 3 4 12
1 5 1 9 9
10
2 9 2 5
EXERCISE: DIVIDING FRACTIONS
Now it’s your turn. Divide these fractions.
1.
2
5
1
2
2.
1
3
6
5
3.
2
5
3 5
Simplifying Fractions
Fractions can be thought of as little division problems. For
instance, 6 3 is the same as 6 3 2. The fraction 1 4 is the same
as 1 4 (which is .25 in decimal form). Now we know that
when we multiply any number by 1, the number stays the same.
For example, 3 5 3 5 1. But if we replace 1 with 2 2 , we get 3 5
3 5 1 3 5 2 2 6
1
. 0 Hence, 3 5 6
1
. 0 Likewise, if we replace 1
with 3 3 , we get 3 5 3 5 3 3 9
1
. 5 In other words, if we multiply the
numerator and denominator by the same number, we get a fraction
that is equal to the first fraction.
For another example,
2
3
2 5
10 3 5 15