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)

Equivalent Fractions

1/2


(ii)

Equivalent Fractions

2/4


(iii)

Equivalent Fractions

4/8


(iv)

8/16


(v)

5/10


(vi)

Equivalent Fractions

10/20


(viii)

6/12


(viii)

Equivalent Fractions

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.

Equivalent Fraction





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.

Equivalent Fraction 1





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.

next three equivalent fractions
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.


Look at the following:

Equivalent Fractions

Look at the figures above.

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

and \(\frac{4}{12}\) represent the same shaded part.

In B the three different fractions \(\frac{1}{4}\), \(\frac{2}{8}\) and \(\frac{4}{16}\) represent the same shaded part.

That is,

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

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


Fractions which represent the same part of a whole thing or which indicates the same number of things in a group are called ‘Equivalent Fractions’.

When we multiply the numerator and denominator of a fraction by the same number (other than zero) we get an equivalent fraction with a higher numerator and denominator.

For example;

\(\frac{1 × 2}{6 × 2}\) = \(\frac{2}{12}\)

\(\frac{1 × 3}{6 × 3}\) = \(\frac{3}{18}\)

\(\frac{1 × 4}{6 × 4}\) = \(\frac{4}{24}\)

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


When we divide the numerator and denominator of a fraction by the same number (other than zero) we get an equivalent fraction with a lower numerator and denominator.

For example:

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

\(\frac{18 ÷ 3}{24 ÷ 3}\) = \(\frac{6}{8}\)

\(\frac{6 ÷ 2}{8 ÷ 2}\) = \(\frac{3}{4}\)

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


2. \(\frac{4}{6}\) = \(\frac{.......}{18}\)

Find the relation between the denominators.

6 × ....... = 18 (since 6 < 18)

6 × 3 = 18

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

Therefore, \(\frac{4}{6}\) = \(\frac{12}{18}\)


3. \(\frac{9}{10}\) = \(\frac{27}{.......}\)

Find the relation between the numerators.

6 × ....... = 27 ? (since 9 < 27)

9 × 3 = 27

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

Therefore, \(\frac{9}{10}\) = \(\frac{27}{30}\)


4. \(\frac{24}{32}\) = \(\frac{.......}{8}\)

32 ÷ 8 = 4 (since 32 >8)

\(\frac{24 ÷ 4}{32 ÷ 4}\) = \(\frac{6}{8}\)

Therefore, \(\frac{24}{32}\) = \(\frac{6}{8}\)


Checking for Equivalence of Fractions:

Cross Product Rule:

If the cross products of two fractions are equal, then they are equivalent fractions.


For example:

1. Is \(\frac{2}{3}\) equivalent to \(\frac{4}{6}\)?



2 × 6 = 12

4 × 3 = 12

Therefore, \(\frac{2}{3}\) is equivalent to \(\frac{4}{6}\)


2. Is \(\frac{2}{4}\) equivalent to \(\frac{3}{5}\)?

Equivalent Fractions

2 × 5 = 10

3 × 4 = 12

Therefore, \(\frac{2}{4}\) is not equivalent to \(\frac{3}{5}\)


Questions and answers on Equivalent Fractions:

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

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

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

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

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


Answers: 

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


Answers:

II. (i) 12

(ii) 63

(iii) 56

(vi) 11

(v) 8

(vi) 33


III. Write two equivalent fractions for the following.

(i) \(\frac{2}{3}\), ........., .........

(ii) \(\frac{4}{5}\), ........., .........

(iii) \(\frac{6}{7}\), ........., .........

(iv) \(\frac{1}{5}\), ........., .........

(v) \(\frac{3}{8}\), ........., .........

(vi) \(\frac{5}{10}\), ........., .........


Answer:

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. Find the missing terms of the following 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) \(\frac{25}{40}\) = \(\frac{.......}{8}\) 


Answer:

IV. (i) 35

(ii) 16

(iii) 4

(iv) 11

(v) 27

(vi) 20

(vii) 33

(viii) 5

(ix) 5


V. Find an equivalent fraction of \(\frac{3}{4}\) with

(i) Numerator 27

(ii) Denominator 28

(iii) Numerator 30

(iv) Denominator 12


Answer:

V. (i) \(\frac{27}{36}\)

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

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

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


VI. Find an equivalent fraction of \(\frac{54}{60}\) with

(i) Numerator 27

(ii) Denominator 10

(iii) Numerator 9

(iv) Denominator 20


Answer:

VI. (i) \(\frac{27}{30}\)

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

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

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


VII. Indicate which of the following pairs of fractions are equivalent:

(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 \(\frac{12}{39}\)


Answer:

VII: (i) Equivalent Fraction

(ii) Equivalent Fraction

(iii) Not Equivalent Fraction

(iv) Not Equivalent Fraction

(v) Equivalent Fraction

Related Concept





4th Grade Math Activities

From Equivalent Fractions to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

    Dec 06, 23 01:23 AM

    2nd Grade Math Worksheet
    2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

    Read More

  2. Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

    Dec 04, 23 02:14 PM

    Different types of Indian Coins
    Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes:

    Read More

  3. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 04, 23 01:50 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More