# Addition and Subtraction of Like Fractions

Here we will learn about addition and subtraction of like fractions.

Addition of Like Fractions:

In order to add two or more like fractions, we may follow the following steps:

**Step I**:

*Obtain the fractions*.

**Step II**:

*Add the numerators of all fractions*.

**Step III**:

*Retain the common denominator of all fractions*.

**Step IV**:

*Write the fraction as Result in Step II / Result in Step III*.

**For Example**:
Add the following fractions.

1.

^{1}/

_{6} +

^{4}/

_{6}
*Solution*:

We have,

^{1}/

_{6} +

^{4}/

_{6}
=

^{(1+4)}/

_{6}
=

^{5}/

_{6}
2.

^{2}/

_{7} +

^{3}/

_{7} +

^{4}/

_{7}
*Solution*:

We have,

^{2}/

_{7} +

^{3}/

_{7} +

^{4}/

_{7}
=

^{(2+3+4)}/

_{7}
=

^{9}/

_{7}
3. 2

^{3}/

_{5} +

^{4}/

_{5} + 1

^{2}/

_{5}
*Solution*:

We have,

2

^{3}/

_{5} +

^{4}/

_{5} + 1

^{2}/

_{5}
=

^{(2 × 5 + 3)}/

_{5} +

^{4}/

_{5} +

^{(1 × 5 + 2)}/

_{5}
=

^{(10 + 3)}/

_{5} +

^{4}/

_{5} +

^{(5 + 2)}/

_{5}
=

^{13}/

_{5} +

^{4}/

_{5} +

^{7}/

_{5}
=

^{(13 + 4 + 7)}/

_{5}
=

^{24}/

_{5}
4. 1

^{1}/

_{4} + 2

^{3}/

_{4} + 7

^{1}/

_{4}
*Solution*:

We have,

1

^{1}/

_{4} + 2

^{3}/

_{4} + 7

^{1}/

_{4}
=

^{(1 × 4 + 1)}/

_{4} +

^{(2 × 4 + 3)}/

_{4} +

^{(7 × 4 + 1)}/

_{4}
=

^{(4 + 1)}/

_{4} +

^{(8 + 3)}/

_{4} +

^{(28 + 1)}/

_{4}
=

^{5}/

_{4} +

^{11}/

_{4} +

^{29}/

_{4}
=

^{(5 + 11 + 29)}/

_{4}
=

^{45}/

_{4}

Subtraction of Like Fractions:

In order to subtract two like fractions, we may follow the following steps:

**Step I**:

*Obtain the two fractions and their numerators*.

**Step II**:

*Subtract the smaller numerator from the bigger numerator*.

**Step III**:

*Retain the common denominator*.

**Step IV**:

*Write the fraction as Result in Step II / Result in Step III*.

**For Example**:
1. Subtract

^{3}/

_{10} from

^{8}/

_{10}
*Solution*:

We have to find,

^{8}/

_{10} –

^{3}/

_{10}
=

^{(8 – 3)}/

_{10}
=

^{5}/

_{10}
=

^{(5 ÷ 5)}/

_{(10 ÷ 5)} [Dividing the numerator and denominator by their HCF (highest common factor) 5].

=

^{1}/

_{2}
2. Compute:

^{5}/

_{12} –

^{7}/

_{12} +

^{11}/

_{12}
*Solution:*
We have,

^{5}/

_{12} –

^{7}/

_{12} +

^{11}/

_{12}
=

^{(5-7+11)}/

_{12}
=

^{(11-2)}/

_{12}
=

^{9}/

_{12}
=

^{(9 ÷ 3)}/

_{(12 ÷ 3)} [Dividing the numerator and denominator by their HCF (highest common factor) 3].

=

^{3}/

_{4}
3. Simplify: 4

^{2}/

_{3} + 1/3 – 4

^{1}/

_{3}
*Solution*:

We have,

4

^{2}/

_{3} + 1/3 – 4

^{1}/

_{3}
=

^{(4 × 3 + 2)}/

_{3} +

^{1}/

_{3} -

^{(4 × 3 + 1)}/

_{3}
=

^{(12+2)}/

_{3} +

^{1}/

_{3} –

^{(12+1)}/

_{3}
=

^{14}/

_{3} +

^{1}/

_{3} -

^{13}/

_{3}
=

^{(14 + 1 – 13)}/

_{3}
=

^{(15 – 13)}/

_{3}
=

^{2}/

_{3}
**For Example**:
Add the following fractions.

1.

^{1}/

_{6} +

^{4}/

_{6}
*Solution*:

We have,

^{1}/

_{6} +

^{4}/

_{6}
=

^{(1+4)}/

_{6}
=

^{5}/

_{6}
2.

^{2}/

_{7} +

^{3}/

_{7} +

^{4}/

_{7}
*Solution*:

We have,

^{2}/

_{7} +

^{3}/

_{7} +

^{4}/

_{7}
=

^{(2+3+4)}/

_{7}
=

^{9}/

_{7}
3. 2

^{3}/

_{5} +

^{4}/

_{5} + 1

^{2}/

_{5}
*Solution*:

We have,

2

^{3}/

_{5} +

^{4}/

_{5} + 1

^{2}/

_{5}
=

^{(2 × 5 + 3)}/

_{5} +

^{4}/

_{5} +

^{(1 × 5 + 2)}/

_{5}
=

^{(10 + 3)}/

_{5} +

^{4}/

_{5} +

^{(5 + 2)}/

_{5}
=

^{13}/

_{5} +

^{4}/

_{5} +

^{7}/

_{5}
=

^{(13 + 4 + 7)}/

_{5}
=

^{24}/

_{5}
4. 1

^{1}/

_{4} + 2

^{3}/

_{4} + 7

^{1}/

_{4}
*Solution*:

We have,

1

^{1}/

_{4} + 2

^{3}/

_{4} + 7

^{1}/

_{4}
=

^{(1 × 4 + 1)}/

_{4} +

^{(2 × 4 + 3)}/

_{4} +

^{(7 × 4 + 1)}/

_{4}
=

^{(4 + 1)}/

_{4} +

^{(8 + 3)}/

_{4} +

^{(28 + 1)}/

_{4}
=

^{5}/

_{4} +

^{11}/

_{4} +

^{29}/

_{4}
=

^{(5 + 11 + 29)}/

_{4}
=

^{45}/

_{4}

**● ****Fraction**

**Representations of Fractions on a Number Line**

**Fraction as Division**

**Types of Fractions**

**Conversion of Mixed Fractions into Improper Fractions**

**Conversion of Improper Fractions into Mixed Fractions**

**Equivalent Fractions**

**Interesting Fact about Equivalent Fractions**

**Fractions in Lowest Terms**

**Like and Unlike Fractions**

**Comparing Like Fractions**

**Comparing Unlike Fractions**

**Addition and Subtraction of Like Fractions**

**Addition and Subtraction of Unlike Fractions**

**Inserting a Fraction between Two Given Fractions**

**Numbers Page **

**6th Grade Page **

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