Download REDUCING FRACTIONS TO THEIR LOWEST TERMS

CHAPTER 3 | FRACTIONS
3.2
REDUCING FRACTIONS
TO THEIR LOWEST TERMS
REDUCING PROPER AND IMPROPER
FRACTIONS TO THEIR LOWEST TERMS
Reducing proper and improper fractions to their lowest terms implies dividing both the numerator
and denominator of the fraction by the same non-zero number, until there is no common factor (other
than 1) for the numerator and the denominator of the fraction.
EXAMPLE
•
2
2 ÷2 1
reduced to its lowest terms is
=
4
4 ÷2 2
•
3
3÷3 1
reduced to its lowest terms is
=
9
9 ÷3 3
EXAMPLE 3.2A - REDUCING FRACTIONS TO THEIR LOWEST TERMS
Reduce
126
to its lowest terms.
30
SOLUTION
126 126 ÷ 2 63 63 ÷ 3 21
=
=
=
=
30
30 ÷ 2 15 15 ÷ 3 5
There is no common factor between 21 and 5.
126
21
reduced to its lowest terms is
.
30
5
However, in a word problem, the improper fraction should be changed to a mixed number in lowest
terms, unless directed in the question to be left as an improper fraction.
Therefore,
Converting the answer to a mixed number in lowest terms, we obtain, 4 15 .
REDUCING MIXED NUMBERS TO THEIR LOWEST TERMS
To reduce mixed numbers to their lowest terms, reduce only the fractional portion to its lowest terms.
EXAMPLE 3.2B - REDUCING MIXED NUMBERS TO THEIR LOWEST TERMS
Reduce 7 126 to its lowest terms,
SOLUTION
7 126 = 7 +
6
6 ÷6
1
=7+
= 7 + = 7 12
12
12 ÷ 6
2
Therefore, 7 126 reduced to its lowest terms is 7 12 .
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3.2 REDUCING FRACTIONS TO THEIR LOWEST TERMS
EQUIVALENT FRACTIONS
The fractions obtained by dividing or multiplying the numerator and the denominator of a fraction by
the same non-zero number are called equivalent fractions.
•
EXAMPLE
In
3
, if we multiply both the numerator and denominator by 2, we obtain,
9
3× 2 6
6
3
= . Therefore,
is an equivalent fraction of .
9 × 2 18
18
9
•
Now, if we divide the numerator and denominator of
6
by 3, we obtain,
18
6 ÷3 2
3 6
2
= . Therefore, ,
, and are equivalent fractions.
18 ÷ 3 6
9 18
6
You can find an equivalent fraction of a mixed number by dividing or multiplying the numerator and
the denominator of the fractional portion of the mixed number by the same non-zero number, as
shown below:
4 28 = 4
2 ÷2
= 4 14
8 ÷2
Therefore, 4 14 is an equivalent mixed number of 4 28 .
EXERCISE 3.2
Answers to the odd numbered problems are available online
In Problems 1 and 2, reduce the fractions or mixed numbers to their lowest terms.
1.
(a)
6
12
(b)
4
20
(c)
3
18
(d)
12
16
(e)
10
100
(f)
15
45
(g) 8 24
2.
(h) 11 93
(i) 2 205
(a)
5
15
(b)
6
14
(c)
9
27
(d)
36
48
(e)
2
20
(f)
10
25
(g) 5 84
(h) 6 164
3.
Find three equivalent fractions of the fractions from Problems 1.
4.
Find three equivalent fractions of the fractions from Problems 2.
(i) 1 124
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