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?

Boys 7/8

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

= 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

= 2/1

= 2

5. Subtract 2/4 from 17/4

Solution:

17/4 – 2/4

= (17 - 2)/4

= 15/4

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)$$\frac{8}{18}$$ - $$\frac{5}{18}$$

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) $$\frac{9}{16}$$ - $$\frac{7}{---}$$ = $$\frac{2}{16}$$

2. (i) 21

(ii) 4

(iii) 19

(iv) 16

You might like these

• Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

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

• Mental Math on Fractions | Fractions Worksheets | Fraction Mental Math

In mental math on fractions we will solve different type of problems on types of fractions, equivalent fractions, fraction in lowest terms, comparison of fractions, fraction in lowest term, types of fractions, addition of fractions, subtraction of fractions and word problems

• Worksheet on Fractions | Questions on Fractions | Representation | Ans

In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced

• Worksheet on Fractions | Fraction Magic Square |Comparing Fractions

In worksheet on fractions, the questions are based on comparing the fractions; arranging the fractions in ascending and descending order; find the sum and the difference of the fractions

• Conversion of Improper Fractions into Mixed Fractions |Solved Examples

In conversion of improper fractions into mixed fractions, we follow the following steps: Step I: Obtain the improper fraction. Step II: Divide the numerator by the denominator

• Conversion of Mixed Fractions into Improper Fractions |Solved Examples

In conversion of mixed fractions into improper fractions, we may follow the following steps: Step I: Obtain the mixed fraction. Let the mixed fraction be 22/5. Step II: Identify the whole number

• Proper Fraction and Improper Fraction |Definition| Examples |Worksheet

What is the difference between proper fraction and improper fraction? Proper fraction: The fractions 1/4, 3/8, 5/11, 9/13, 14/25, etc. are the fractions where the numerators are smaller than

• Like and Unlike Fractions | Like Fractions |Unlike Fractions |Examples

Like and unlike fractions are the two groups of fractions: (i) 1/5, 3/5, 2/5, 4/5, 6/5 (ii) 3/4, 5/6, 1/3, 4/7, 9/9 In group (i) the denominator of each fraction is 5, i.e., the denominators of the fractions are equal. The fractions with the same denominators are called

• Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerator < denominator). Two parts are shaded in the above diagram.

• Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the common denominator.

• Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a number to convert them to like fractions. Let us consider some of the

• Comparison of Fractions having the same Numerator|Ordering of Fraction

In comparison of fractions having the same numerator the following rectangular figures having the same lengths are divided in different parts to show different denominators. 3/10 < 3/5 < 3/4 or 3/4 > 3/5 > 3/10 In the fractions having the same numerator, that fraction is

• Comparison of Like Fractions | Comparing Fractions | Like Fractions

Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example $$\frac{7}{13}$$ > $$\frac{2}{13}$$ because 7 > 2. In comparison of like fractions here are some

• Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1(one), then the fraction is said to be in its simple form or in lowest

• Fraction as a Part of Collection | Pictures of Fraction | Fractional

How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it is folded into two halves, each half will have 7 rectangles. So, we can say

• Numerator and Denominator of a Fraction | Numerator of the Fraction

What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.

• Fraction of a Whole Numbers | Fractional Number |Examples with Picture

Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One part is shaded, i.e., one-fourth of the shape is shaded and three

• Identification of the Parts of a Fraction | Fractional Numbers | Parts

We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

Related Concepts

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.

Recent Articles

1. Shifting of Digits in a Number |Exchanging the Digits to Another Place

May 19, 24 06:35 PM

What is the Effect of shifting of digits in a number? Let us observe two numbers 1528 and 5182. We see that the digits are the same, but places are different in these two numbers. Thus, if the digits…

2. Formation of Greatest and Smallest Numbers | Arranging the Numbers

May 19, 24 03:36 PM

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number…

3. Formation of Numbers with the Given Digits |Making Numbers with Digits

May 19, 24 03:19 PM

In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

4. Arranging Numbers | Ascending Order | Descending Order |Compare Digits

May 19, 24 02:23 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…