In addition and subtraction of unlike fractions, we first convert them into corresponding equivalent like fractions and then they are added or subtracted.

Following steps are used to do the same.

**Step I**:

*Obtain the fractions and their denominators*.

**Step II**:

*Find the LCM (least common multiple) of the denominators*.

**Step III:**

*Convert each fraction into an equivalent fraction having its denominator equal to the LCM (least common multiple) obtained in Step II.*

**Step IV:**

*Add or subtract like fractions obtained in Step III.***For Example:****1.** Add ²/₃ and ³/₇.*Solution*:

The LCM (least common multiple) of the denominators 3 and 7 is 21.

So, we convert the given fractions into equivalent fractions with denominator 21.

We have,

^{2}/_{3}+^{3}/_{7}

=^{(2 × 7)}/_{(3 × 7)}+^{(3 × 3)}/_{(7 × 3)}

[since 21 ÷ 3 = 7 and 21 ÷ 7 = 3]

=^{14}/_{21}+^{9}/_{21}

=^{(14 + 9)}/_{21}

=^{23}/_{21}

The LCM (least common multiple) of the denominators 6 and 8 is 24.

So, we convert the given fractions into equivalent fractions with denominator 24.

We have,

=^{1}/_{6}=^{(1 × 4)}/_{(6 × 4)}=^{4}/_{24}[since 24 ÷ 6 = 4]

and,^{3}/_{8}=^{(3 × 3)}/_{(8 × 3)}=^{9}/_{24}[since 24 ÷ 8 = 3]

Thus,^{1}/_{6}+^{3}/_{8}=^{4}/_{24}+^{9}/_{24}

=^{(4 + 9)}/_{24}

=^{13}/_{24}

We have,

2^{4}/_{5}=^{(2 × 5 + 4)}/_{5}=^{(10 + 4)}/_{5}=^{14}/_{5}

and, 3^{5}/_{6}=^{(3 × 6 + 5)}/_{6}=^{23}/_{6}

Now, we will compute^{14}/_{5}+^{23}/_{6}

The LCM (least common multiple) of the denominators 5 and 6 is 30.

So, we convert the given fractions into equivalent fractions with denominator 30.

We have,

=^{14}/_{5}=^{(14 × 6)}/_{(5 × 6)}=^{84}/_{30}[since 30 ÷ 5 = 6]

and,^{23}/_{6}=^{(23 × 5)}/_{(6 × 5)}=^{115}/_{30}[since 30 ÷ 6 = 5]

Thus,^{14}/_{5}+^{23}/_{6}=^{84}/_{30}+^{115}/_{30}

=^{(84 + 115)}/_{30}

=^{199}/_{30}

= 6¹⁹/₃₀

The LCM (least common multiple) of the denominators 24 and 16 is 48.

[Therefore, LCM = 2 × 2 × 2 × 2 × 3 = 48]

So, we convert the given fractions into equivalent fractions with denominator 48.

We have,

=^{17}/_{24}=^{(17 × 2)}/_{(24 × 2)}=^{34}/_{48}[since 48 ÷ 24 = 2]

and,^{15}/_{16}=^{(15 × 3)}/_{(16 × 3)}=^{45}/_{48}[since 48 ÷ 16 = 3]

Clearly,^{45}/_{48}>^{34}/_{48}

Therefore,^{15}/_{16}>^{17}/_{24}

Hence, difference =^{15}/_{16}–^{17}/_{24}

=^{45}/_{48}–^{34}/_{48}

=^{(45 – 34)}/_{48}

=^{11}/_{48}.

We have,

4^{2}/_{3}– 3^{1}/_{4}+ 2^{1}/_{6}

=^{(4 × 3 + 2)}/_{3}–^{(3 × 4 + 1)}/_{4}+^{(2 × 6 +1)}/_{6}

=^{(12 + 2)}/_{3}–^{(12 +1)}/_{4}+^{(12+1)}/_{6}

=^{14}/_{3}–^{13}/_{4}+^{13}/_{6}

The LCM (least common multiple) of the denominators 3, 4 and 6 is 12.

[Therefore, LCM = 2 × 2 × 3 = 12]

So, we convert the given fractions into equivalent fractions with denominator 12.

We have,

=^{(14 × 4)}/_{(3 × 4)}–^{(13 × 3)}/_{(4 × 3)}+^{(13 × 2)}/_{(6 × 2)}

=^{56}/_{12}–^{39}/_{12}+^{26}/_{12}

=^{(56 – 39 + 26)}/_{12}

=^{(82 – 39)}/_{12}

=^{43}/_{12}

= 3⁷/₁₂

**● ****Fraction**

**Representations of Fractions on a Number Line**

**Conversion of Mixed Fractions into Improper Fractions**

**Conversion of Improper Fractions into Mixed Fractions**

**Interesting Fact about Equivalent 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****From Addition and Subtraction of Unlike Fractions to HOME PAGE**

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