Page 28 - ICSE Math 7

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Example 1: Convert 2 to improper fraction.
5
3
Solution: 2 = (2 × 5) + 3 = 10 + 3 = 13
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Example 2: Convert 19 to mixed fraction. 2
7 7 19

Solution: 19 = 2 5 –14
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Simple fraction

In a simple fraction, the numerator and denominator are integers. It is also known as a common or
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vulgar fraction. For example, , , and 21 are simple fractions.
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Complex fraction
A fraction whose numerator or denominator or both are fractions is known as a complex fraction.
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For example, , , are complex fractions.
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Equivalent fractions
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1
2
Fractions having the same value are known as equivalent fractions. For example, , , and 4
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are equivalent fractions as they are equal in value. If the numerator and denominator of a fraction are
multiplied or divided by the same non-zero number, then we get an equivalent fraction. Two fractions
c
a and are equivalent if ad = bc.
b d
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Example 3: Write an equivalent fraction of in which numerator is 49.
9
7
Solution: To make the numerator 49, multiply by 7.
7 7 × 7 49 9
= = Try These
9 9 × 7 63
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Thus, the required equivalent fraction is 49 . 1. Fill in the box to make
63 equivalent to  . 7
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Example 4: Verify that and are equivalent fractions. 2. Write two equivalent
20 180 fractions for .
3
c
a
Solution: Two fractions and are equivalent if ad = bc. 5
b d
Here, a = 16, b = 20, c = 144 and d = 180.
ad = 16 × 180 = 2,880 and bc = 20 × 144 = 2,880
16 144
\ and are equivalent fractions.
20 180

Reducing a fraction to its simplest form
A fraction is in its simplest form or lowest terms if its numerator and denominator have no common
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factor except 1. For example, , and are fractions in their simplest form.
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A fraction can be reduced to its simplest form by two methods.
(a) Prime factorization method (b) HCF method

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