The fractions having the identical worth are referred to as equal fractions. Their numerator and denominator will be totally different however, they signify the identical half of an entire.

Think about the next:

(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 will see the shade portion with respect to the entire form within the figures from (i) to (viii)**

In; (i) *Shaded to entire form is half to entire* i.e., ^{1}/_{2}

(ii) *Shaded to entire form is 2 to fourth* i.e., ^{2}/_{4} = ^{1}/_{2}

(iii) *Shaded to entire form is 4 to eighth* i.e., ^{4}/_{8} = ^{1}/_{2}

(iv) *Shaded to entire form is 8 to sixteenth* i.e., ^{8}/_{16} = ^{1}/_{2}

(v) *Shaded to entire form is 5 to tenth* i.e., ^{5}/_{10} = ^{1}/_{2}

(vi) *Shaded to entire form is 10 to twentieth* i.e., ^{10}/_{20} = ^{1}/_{2}

(vii) *Shaded to entire form is 6 to twelfth* i.e., ^{6}/_{12} = ^{1}/_{2}

(viii) *Shaded to entire form is 3 to sixth* i.e., ^{3}/_{6} = ^{1}/_{2}

Thus, 1/2, 2/4, 4/8, 8/16, 5/10, 10/20, 6/12, 3/6, and so forth., every fraction represents half portion of the form, that are all equal. All have totally different numerator and denominator however all of them have the identical worth as a result of they signify the identical shaded space i.e., half of the rectangle.

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

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

**The
fractions having totally different numerators and denominators however representing
equal worth or magnitude are referred to as equal fractions.**

**Word:**

The fraction 1/2 and a pair of/4 and 4/8 present the identical quantity of shaded or coloured elements. 1/2 and a pair of/4 and 4/8 are equal fractions.

Equal fractions are fractions which have totally different types however the identical worth.

Constructing Equal Fractions:

**1. ** Change 2/5 to an equal fraction with denominator 15.

**Word:**

Multiply numerator and denominator by the identical quantity to get the required denominator.

**2. ** Change 9/12 to an equal fraction with denominator 4.

**Word:**

To seek out an equal fraction with smaller denominator, you’ll be able to divide the numerator and denominator with the identical quantity.

**3. ** We will construct equal fraction with multiples of numerator and denominator.

Write the following three equal fractions.

**Word:**

Equal fractions have the identical worth.

**Equal fraction will be constructed to very massive numbers.**

Equal fraction will be diminished to the bottom time period.

Have a look at the figures above.

In A the three totally different fractions (frac{1}{3}), (frac{2}{6})

and (frac{4}{12}) signify the identical shaded half.

In B the three totally different fractions (frac{1}{4}), (frac{2}{8}) and (frac{4}{16}) signify the identical shaded half.

That’s,

(frac{1}{3}) = (frac{2}{6}) = (frac{4}{12});

(frac{1}{4}) = (frac{2}{8}) = (frac{4}{16})

Fractions which signify the identical half of an entire factor or which signifies the identical variety of issues in a gaggle are referred to as ‘Equal Fractions’.

Once we multiply the numerator and denominator of a fraction by the identical quantity (apart from zero) we get an equal fraction with the next numerator and denominator.

**For instance;**

(frac{1 × 2}{6 × 2}) = (frac{2}{12})

(frac{1 × 3}{6 × 3}) = (frac{3}{18})

(frac{1 × 4}{6 × 4}) = (frac{4}{24})

(frac{1}{6}) = (frac{2}{12}) = (frac{3}{18}) = (frac{4}{24})

Once we divide the numerator and denominator of a fraction by the identical quantity (apart from zero) we get an equal fraction with a decrease numerator and denominator.

(frac{36 ÷ 2}{48 ÷ 2}) = (frac{18}{24})

(frac{18 ÷ 3}{24 ÷ 3}) = (frac{6}{8})

(frac{6 ÷ 2}{8 ÷ 2}) = (frac{3}{4})

(frac{3}{4}) = (frac{6}{8}) = (frac{18}{24}) = (frac{36}{48})

**For instance:**

**1.** (frac{4}{6}) = (frac{…….}{18})

Discover the relation between the denominators.

6 × ……. = 18 (since 6 < 18)

6 × 3 = 18

Subsequently, (frac{4 × 3}{6 × 3}) = (frac{12}{18})

Subsequently, (frac{4}{6}) = (frac{12}{18})

**2.** (frac{9}{10}) = (frac{27}{…….})

Discover the relation between the numerators.

6 × ……. = 27 ? (since 9 < 27)

9 × 3 = 27

Subsequently, (frac{9 × 3}{10 × 3}) = (frac{27}{30})

Subsequently, (frac{9}{10}) = (frac{27}{30})

**3.** (frac{24}{32}) = (frac{…….}{8})

32 ÷ 8 = 4 (since 32 >8)

(frac{24 ÷ 4}{32 ÷ 4}) = (frac{6}{8})

Subsequently, (frac{24}{32}) = (frac{6}{8})

**Checking for Equivalence of Fractions:**

Cross Product Rule:

If the cross merchandise of two fractions are equal, then they’re equal fractions.

**For instance:**

**1. Is (frac{2}{3}) equal to (frac{4}{6})?**

2 × 6 = 12

4 × 3 = 12

Subsequently, (frac{2}{3}) is equal to (frac{4}{6})

**2. Is (frac{2}{4}) equal to (frac{3}{5})?**

2 × 5 = 10

3 × 4 = 12

Subsequently, (frac{2}{4}) shouldn’t be equal to (frac{3}{5})

Questions and solutions on Equal Fractions:

**I.** **Discover 4 equal fractions for the given fractions by
multiplying.**

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

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

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

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

**Solutions: **

**I.** (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})

**II.** **Fill the bins to make equal 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})

**Solutions:**

**II.** (i) 12

(ii) 63

(iii) 56

(vi) 11

(v) 8

(vi) 33

**III. Write two equal fractions for the next.**

(i) (frac{2}{3}), ………, ………

(ii) (frac{4}{5}), ………, ………

(iii) (frac{6}{7}), ………, ………

(iv) (frac{1}{5}), ………, ………

(v) (frac{3}{8}), ………, ………

(vi) (frac{5}{10}), ………, ………

**Reply:**

**III. **(i) (frac{4}{6}), (frac{6}{9})

(ii) (frac{8}{10}), (frac{20}{25})

(iii) (frac{24}{28}), (frac{36}{42})

(iv) (frac{3}{15}), (frac{10}{50})

(v) (frac{9}{24}), (frac{21}{56})

(vi) (frac{5}{10}), (frac{3}{8})

**IV. Discover the lacking phrases of the next fractions.**

(i) (frac{1}{7}) = (frac{5}{…….})

(ii) (frac{3}{4}) = (frac{12}{…….})

(iii) (frac{25}{100}) = (frac{1}{…….})

(iv) (frac{55}{100}) = (frac{…….}{20})

(v) (frac{3}{7}) = (frac{…….}{63})

(vi) (frac{5}{6}) = (frac{…….}{24})

(vii) (frac{6}{11}) = (frac{18}{…….})

(viii) (frac{15}{48}) = (frac{…….}{16})

(ix) (frac{25}{40}) = (frac{…….}{8})

**Reply:**

**IV. **(i) 35

(ii) 16

(iii) 4

(iv) 11

(v) 27

(vi) 20

(vii) 33

(viii) 5

(ix) 5

**V. Discover an equal fraction of (frac{3}{4}) with**

(i) Numerator 27

(ii) Denominator 28

(iii) Numerator 30

(iv) Denominator 12

**Reply:**

**V. **(i) (frac{27}{36})

(ii) (frac{21}{28})

(iii) (frac{30}{40})

(iv) (frac{9}{12})

**VI. Discover an equal fraction of (frac{54}{60}) with**

(i) Numerator 27

(ii) Denominator 10

(iii) Numerator 9

(iv) Denominator 20

**Reply:**

**VI. **(i) (frac{27}{30})

(ii) (frac{9}{10})

(iii) (frac{9}{10})

(iv) (frac{18}{20})

**VII. Point out which of the next pairs of fractions are equal:**

(i) (frac{3}{5}) and (frac{9}{15})

(ii) (frac{2}{8}) and (frac{10}{40})

(iii) (frac{5}{7}) and (frac{25}{42})

(iv) (frac{9}{11}) and (frac{27}{34})

(v) (frac{4}{13}) and (frac{12}{39})

**Reply:**

**VII:** (i) Equal Fraction

(ii) Equal Fraction

(iii) Not Equal Fraction

(iv) Not Equal Fraction

(v) Equal Fraction

**Associated Idea**

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