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.
^{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}
= ^{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}
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}
= ^{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
= ^{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}.
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}
= ^{(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
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