# How to Reduce Fractions to Their Lowest Terms

## Expressing Fractions in Lowest Terms

When a thing or unit is divided into equal parts, the number expressing the relation of one or more of the equal parts to the total number of equal parts is called a fraction. The number above the fraction bar is called the numerator. The number below the fraction bar is called the denominator. When the numerator and denominator have no common factor except 1, the fraction is in "simplest form or in lowest terms." When the 4 and 8 of the fraction 4/8 are each:

#### Look at a Multiplication Chart to Find What Number Each Fraction has in Common to Reduce

(1.) 4/8 = 4/8 ÷ 2/2 = 2/4

(1.) Divided by 2, we get the equivalent fraction 2/4.

(2.) 4/8 = 4/8 ÷ 4/4 = 1/2

(2.) Divided by 4, we get the equivalent fraction 1/2.

Then when the numerator and denominator of any fraction are each divided by the same number, expect by zero, the result is an equivalent fraction. To express a fraction in lowest terms:

(a.) We factor the numerator and denominator, using as one of the factors the greatest factor common to both. (Use whole numbers other than 1 or 0.)

(b.) Then we divide both the numerator and denominator by this common factor.

These examples look better written on paper. The multiplicative identity on (1) may be used as:

Express 30/48 in lowest terms: 30/48 = 5/8 x 6/6 or 30/48 = 5/8 x 6/6 = 5/8 x 1 = 5/8

## How to Reduce Fractions to Their Lowest Terms

Express each of the following in lowest terms:

5/10 = 1/5 x 5/5 = 1/5
7/56 =
5/60 =
2/16 =
11/77 =
3/15 =
6/42 =
5/20 =
6/12 =
9/45 =
12/36 =
14/42 =
25/100 =
8/64 =
15/75 =
Expressing Fractions in Lowest Terms

## Figure out these fractions on paper

◊ Find which fractions are equal to each other in each group -

Look at a Multiplication Chart to Find What Number Each Fraction has in Common to Reduce to Lowest Terms:

a. 6/8

b. 12/15

c. 18/24

d. 9/12

e. 15/25

f. 6/9

g. 4/6

h. 14/21

i. 10/32

j. 9/24

k. 21/56

◊ Which fractions are not expressed in lowest terms?

a. 3/4

b. 3/5

c. 3/6

d. 3/8

e. 4/7

f. 5/8

g. 4/9

h. 6/9

i. 9/10

j. 7/10

k. 5/10,

l. 3/10

m. 5/8

n. 11/12

o. 21/28

p. 25/32

q. 8/15

r. 12/35,

s. 9/45,

t. 17/20

See results

0

2

2

4

3

258

26