Subtraction of Fractions having the Same Denominator

In subtraction of fractions having the same denominator, we just need to subtract the numerators of the fractions.

To find the difference between like fractions we subtract the smaller numerator from the greater numerator. The denominator of the required fraction is the common denominator of the given fractions.

Difference of two fractions with like denominators = \(\frac{\textrm{Difference of Numerators}}{\textrm{Common Denominator}}\)

 

For example:

\(\frac{5}{7}\) - \(\frac{2}{7}\) = \(\frac{5 - 2}{7}\) = \(\frac{3}{7}\)


Follow the steps of subtraction of like fractions:

We can subtract in a similar way. 7/8 of the class are boys.

3/8 of the class are girls. By how much fraction are the boys more?

Subtraction of Fractions

Boys 7/8


Subtraction of Like Fraction

Girls 3/8


7/8 - 3/8 

= (7 - 3)/8 

= 4/8

The difference is 4/8 or 1/2

We can also reduce the fraction to the lowest term. 

4/8 ÷ 4/4 

= 1/2


Examples of subtracting fractions with the same denominator:

1. Subtract 3/8 from 7/8

Solution:

7/8 – 3/8

= (7 - 3)/8

subtracting fractions with the same denominator





= 1/2



2. Subtract 5/6 from 11/6

Solution:

11/6 – 5/6

= (11 - 5)/6

= 6/6

= 1/1

= 1



3. Subtract 7/9 from 11/9

Solution:

11/9 – 7/9

= (11 - 7)/9

= 4/9


4. Subtract 4/6 from 16/6

Solution:

16/6 – 4/6

= (16 - 4)/6

Subtraction of Fractions




= 2/1

= 2



5. Subtract 2/4 from 17/4

Solution:

17/4 – 2/4

= (17 - 2)/4

= 15/4

Subtraction of Fractions having the Same Denominator


Subtraction of Like Fractions:

6. Subtract \(\frac{7}{17}\) - \(\frac{5}{17}\)    

\(\frac{7}{17}\) - \(\frac{5}{17}\) = \(\frac{7 - 5}{17}\)

            = \(\frac{2}{17}\)  


7. Subtract \(\frac{13}{23}\) - \(\frac{9}{23}\)   

\(\frac{13}{23}\) - \(\frac{9}{23}\) = \(\frac{13 - 9}{23}\)

            = \(\frac{4}{23}\)  

Subtraction of Fractions with the Same (Like) Denominator
To subtract fractions with like denominator, we subtract the smaller numerator from the greater to obtain the numerator of the required fraction.


8. Subtract \(\frac{3}{8}\) from \(\frac{9}{8}\)

Solution:

   \(\frac{9}{8}\) + \(\frac{3}{8}\)

= \(\frac{9 - 3}{8}\)

= \(\frac{6}{8}\)


9. Subtract \(\frac{5}{14}\) from \(\frac{9}{14}\)

Solution:

    \(\frac{9}{14}\) - \(\frac{5}{14}\)

= \(\frac{9 - 5}{14}\)

= \(\frac{4}{14}\)


Worksheet on Like Fraction:

1. Subtract the following Like Fractions:

(i) \(\frac{12}{17}\) - \(\frac{5}{17}\)

(ii) \(\frac{17}{23}\) - \(\frac{4}{23}\)

(iii) \(\frac{9}{13}\) - \(\frac{3}{13}\)

(iv) \(\frac{3}{11}\) - \(\frac{2}{11}\)

(v) \(\frac{5}{17}\) - \(\frac{2}{17}\)

(vi) \(\frac{11}{16}\) - \(\frac{7}{16}\)

(vii) \(\frac{9}{24}\) - \(\frac{5}{24}\)

(viii) \(\frac{15}{24}\) - \(\frac{14}{24}\)

(ix) \(\frac{7}{12}\) - \(\frac{4}{12}\)

(x) \(\frac{8}{16}\) - \(\frac{5}{16}\)

(xi) \(\frac{9}{14}\) - \(\frac{5}{14}\)

(xii)\(\frac{8}{18}\) - \(\frac{5}{18}\)


Answer:

1. (i) \(\frac{7}{17}\)

(ii) \(\frac{13}{23}\)

(iii) \(\frac{6}{13}\)

(iv) \(\frac{1}{11}\)

(v) \(\frac{3}{17}\)

(vi) \(\frac{4}{16}\)

(vii) \(\frac{4}{24}\)

(viii) \(\frac{1}{24}\)

(ix) \(\frac{3}{12}\)

(x) \(\frac{3}{16}\)

(xi) \(\frac{4}{14}\)

(xii)\(\frac{3}{18}\)



2. Fill in the blanks:

(i) \(\frac{8}{21}\) - \(\frac{3}{---}\) = \(\frac{5}{21}\)

(ii) \(\frac{5}{7}\) - \(\frac{---}{7}\) = \(\frac{1}{7}\)

(iii) \(\frac{5}{19}\) - \(\frac{3}{19}\) = \(\frac{2}{---}\)

(iv) \(\frac{9}{16}\) - \(\frac{7}{---}\) = \(\frac{2}{16}\)



Answer:

2. (i) 21

(ii) 4

(iii) 19

(iv) 16

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