Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 5: Fractions 63

Multiply numerator times numerator and denominator times denominator, using the new
numbers.

MATH TRAP

When cancelling, remember to divide a numerator and a denominator by the same

number. Never divide two numerators or two denominators.

Let’s look at some examples. First, we’ll walk through^38349 .The basic rules says to multiply 3

times 4 and 8 times 9, giving the fraction^1272 , which reduces to^16. However, you can cancel before

multiplying. Divide 3 into both 3 and 9, and divide 4 into both 4 and 8. The problem turns into
1
2

1

3

(^3).
Let’s try one with a mixed number. That’s a whole number plus a fraction, but you can turn it
into an improper fraction by finding the proper disguise for the whole number part.
Divide 1141437.
Whenever a multiplication or division problem involves a mixed number, convert to an improper
fraction immediately. The 1 is equal to
14
14 and the additional
1
14 makes
15
14 , so your problem is
really
15
14
3
(^47).
To divide, you need to multiply by the reciprocal of the divisor, or invert the divisor,^37 , and
multiply. The problem^1514473 is equivalent to^1514373. Cancel before you multiply. Divide both 15
and 3 by 3, and divide 7 and 14 by 7.
The product^52 is an improper fraction, and that’s fine. If you’d rather see it as a mixed number,
remember the denominator says the whole was broken into two pieces, broken in halves. You have
5 of those, so you can piece together 2 wholes and have 1 half left.
8
9
7
12
8
9
7
12
27
93
14
27
2
3
335 33 55
3
8
4
9
3
8
4
9
3
8
4
9
11
23
1
6
1
3
1
2
1
3
33 3^3
3
15
14
7
3
15
14
7
3
15
14
7
3
51
21
5
2
5
1
5
2
1
1
33 3^3
3
5
2 2
1
2 2
1
(^5152)