# Addition and Subtraction of Fractions

#### Summary

**Addition of like fractions**

Steps to add like fractions:

Step 1: Add the numerators of the fractions to get the numerator of the resultant fraction.

Step 2: Use the common denominator of the like fractions as the denominator of the resultant fraction.

e.g. Find the sum of $\frac{\text{1}}{\text{7}}$, $\frac{\text{2}}{\text{7}}$ and $\frac{\text{3}}{\text{7}}$

Sol: $\frac{\text{1}}{\text{7}}$ + $\frac{\text{2}}{\text{7}}$ + $\frac{\text{3}}{\text{7}}$ = $\frac{\text{1 + 2 + 3}}{\text{7}}$ = $\frac{\text{6}}{\text{7}}$

**Subtraction of like fractions**

Steps to subtract two like fractions:

Step 1: Subtract the numerators of the fractions to get the numerator of the resultant fraction.

Step 2: Use the common denominator of the like fractions as the denominator of the resultant fraction.

e.g. Find the difference between $\frac{\text{3}}{\text{7}}$ and $\frac{\text{1}}{\text{7}}$.

Sol: $\frac{\text{3}}{\text{7}}$ – $\frac{\text{1}}{\text{7}}$ = $\frac{\text{3 - 1}}{\text{7}}$ = $\frac{\text{2}}{\text{7}}$

**Addition of unlike fractions**

Steps to add unlike fractions:

Step 1: Find the equivalent fractions of the given unlike fractions with the same denominator.

Step 2: Add the numerators of the fractions to get the numerator of the resultant fraction.

Step 3: Use the common denominator of the obtained like fractions as the denominator of the resultant fraction.

e.g. Find the sum of $\frac{\text{5}}{\text{18}}$ and $\frac{\text{4}}{\text{15}}$.

Sol: LCM of 18 and 15 = 90.

$\frac{\text{5}}{\text{18}}$ = $\frac{\text{5 x 5}}{\text{18 x 5}}$ = $\frac{\text{25}}{\text{90}}$

$\frac{\text{4}}{\text{15}}$ = $\frac{\text{4 x 6}}{\text{15 x 6}}$ = $\frac{\text{24}}{\text{90}}$

$\frac{\text{5}}{\text{18}}$ + $\frac{\text{4}}{\text{15}}$ = $\frac{\text{25}}{\text{90}}$ + $\frac{\text{24}}{\text{90}}$

= $\frac{\text{25 + 24}}{\text{90}}$

= $\frac{\text{49}}{\text{90}}$

**Subtraction of unlike fractions**

Steps to subtract two unlike fractions:

Step 1: Find the equivalent fractions of the given unlike fractions with the same denominator.

Step 2: Subtract the numerators of the fractions to get the numerator of the resultant fraction.

Step 3: Use the common denominator of the obtained like fractions as the denominator of the resultant fraction.

e.g. Find the difference between $\frac{\text{5}}{\text{18}}$ and $\frac{\text{4}}{\text{15}}$.

Sol: LCM of 18 and 15 = 90.

$\frac{\text{5}}{\text{18}}$ = $\frac{\text{5 x 5}}{\text{18 x 5}}$ = $\frac{\text{25}}{\text{90}}$

$\frac{\text{4}}{\text{15}}$ = $\frac{\text{4 x 6}}{\text{15 x 6}}$ = $\frac{\text{24}}{\text{90}}$

$\frac{\text{5}}{\text{18}}$ – $\frac{\text{4}}{\text{15}}$ = $\frac{\text{25}}{\text{90}}$ – $\frac{\text{24}}{\text{90}}$

= $\frac{\text{25 - 24}}{\text{90}}$

= $\frac{\text{1}}{\text{90}}$

**Addition or subtraction of mixed fractions**

Two mixed fractions can be added or subtracted by adding or subtracting the whole numbers of the two fractions, and then adding or subtracting the fractional parts together. Two mixed fractions can also be converted into improper fractions and then added or subtracted.

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#### Questions & Answers*arrow_upward*

### 1 . whose numerator and denominator add up to 10

(c) Fractions whose numerator and denominator add upto to 10 are

1/9, 2/8, 3/7, 4/6, 5/4, 7/3 etc

### 2 . Write prime numbers between 50 and 70

The prime nos. between 50 and 70 are as follows:

53,59,61,67.

### 3 . If javed was given 5 upon 7 of a basket of oranges

ORANGES IN BASKETS=1

GIVEN TO JAVED=5/7

LEFT=1-(5/7)=2/7

### 4 . How to teach the maths to slow learners?

3/4+5/9

=3*9/4*9+5*4/9*4

=27/36+20/36

=27+20/36

=47/36

=1.30555

### 5 . Whose denominator is 4 more than the numerator.

Let the numerator be x then denominator will be (x + 4)

Hence the fraction is [x/(x + 4)]

Put x = 1, the fraction becomes 1/...