Page 18 - MarceAlgebra Demystified

CHAPTER 1 Fractions 5

Solutions

7 1 7 4 28
1: ¼ ¼
6 4 6 1 6
8 6 8 5 40
2: ¼ ¼
15 5 15 6 90
5 9 5 10 50
3: ¼ ¼
3 10 3 9 27

40 2 40 3 120
4: ¼ ¼
9 3 9 2 18
3 30 3 4 12
5: ¼ ¼
7 4 7 30 210
2 4 2 4 3 12
6: 4 ¼ ¼ ¼
3 1 3 1 2 2

10 10 3 10 1 10
7: 3 ¼ ¼ ¼
21 21 1 21 3 63

Reducing Fractions

When working with fractions, you are usually asked to ‘‘reduce the fraction
to lowest terms’’ or to ‘‘write the fraction in lowest terms’’ or to ‘‘reduce the
fraction.’’ These phrases mean that the numerator and denominator have no
common factors. For example, 2 is reduced to lowest terms but 4 is not.
3 6
Reducing fractions is like fraction multiplication in reverse. We will first use
the most basic approach to reducing fractions. In the next section, we will
learn a quicker method.
First write the numerator and denominator as a product of prime
numbers. Refer to the Appendix if you need to review how to find the
prime factorization of a number. Next collect the primes common to both
the numerator and denominator (if any) at beginning of each fraction. Split
each fraction into two fractions, the first with the common primes. Now the
fraction is in the form of ‘‘1’’ times another fraction.