# Equivalent Fractions

The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole.

Consider the following:

(i) 1/2

(ii) 2/4

(iii) 4/8

(iv) 8/16

(v) 5/10

(vi) 10/20

(viii) 6/12

(viii) 3/6

We can see the shade portion with respect to the whole shape in the figures from (i) to (viii)

In; (i) Shaded to whole shape is half to whole             i.e., 1/2

(ii) Shaded to whole shape is 2 to fourth                   i.e., 2/4 = 1/2

(iii) Shaded to whole shape is 4 to eighth                   i.e., 4/8 = 1/2

(iv) Shaded to whole shape is 8 to sixteenth              i.e., 8/16 = 1/2

(v) Shaded to whole shape is 5 to tenth                    i.e., 5/10 = 1/2

(vi) Shaded to whole shape is 10 to 20th                   i.e., 10/20 = 1/2

(vii) Shaded to whole shape is 6 to 12th                    i.e., 6/12 = 1/2

(viii) Shaded to whole shape is 3 to 6th                     i.e., 3/6 = 1/2

Thus, 1/2, 2/4, 4/8, 8/16, 5/10, 10/20, 6/12, 3/6, etc., each fraction represents half portion of the shape, which are all equal. All have different numerator and denominator but they all have the same value because they represent the same shaded area i.e., half of the rectangle.

So, 1/2, 2/4, 4/8, 8/16, 5/10, 10/20, 6/12, 3/6 are equivalent fractions.

We can express it as, 1/2 = 2/4 = 4/8 = 8/16 = 5/10 = 10/20 = 6/12 = 3/6 = 1/2.

The fractions having different numerators and denominators but representing equal value or magnitude are called equivalent fractions.

Note:

The fraction 1/2 and 2/4 and 4/8 show the same amount of shaded or colored parts. 1/2 and 2/4 and 4/8 are equivalent fractions.
Equivalent fractions are fractions that have different forms but the same value.

Building Equivalent Fractions:

1. Change 2/5 to an equivalent fraction with denominator 15. Note:

Multiply numerator and denominator by the same number to get the required denominator.

2. Change 9/12 to an equivalent fraction with denominator 4. Note:

To find an equivalent fraction with smaller denominator, you can divide the numerator and denominator with the same number.

3. We can build equivalent fraction with multiples of numerator and denominator.

Write the next three equivalent fractions. Note:

Equivalent fractions have the same value.

Equivalent fraction can be built to very large numbers.

Equivalent fraction can be reduced to the lowest term.

Questions and answers on Equivalent Fractions:

1. Find 4 equivalent fractions for the given fractions by multiplying.

(i) $$\frac{3}{7}$$

(ii) $$\frac{2}{9}$$

(iii) $$\frac{4}{5}$$

(vi) $$\frac{7}{11}$$

1. (i) $$\frac{6}{14}$$, $$\frac{9}{21}$$, $$\frac{12}{28}$$, $$\frac{15}{35}$$

(ii) $$\frac{4}{18}$$, $$\frac{6}{27}$$, $$\frac{8}{36}$$, $$\frac{10}{45}$$

(iii) $$\frac{8}{10}$$, $$\frac{12}{15}$$, $$\frac{16}{20}$$, $$\frac{20}{25}$$

(vi) $$\frac{14}{22}$$, $$\frac{21}{33}$$, $$\frac{28}{44}$$, $$\frac{35}{55}$$

2. Fill the boxes to make equivalent fractions:

(i) $$\frac{3}{4}$$ = $$\frac{……}{16}$$

(ii) $$\frac{5}{9}$$ = $$\frac{35}{……}$$

(iii) $$\frac{7}{8}$$ = $$\frac{……}{64}$$

(vi) $$\frac{7}{……}$$ = $$\frac{63}{99}$$

(v) $$\frac{2}{13}$$ = $$\frac{……}{51}$$

(vi) $$\frac{11}{17}$$ = $$\frac{……}{51}$$

2. (i) 12

(ii) 63

(iii) 56

(vi) 11

(v) 8

(vi) 33

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