Simplification of Fractions
In simplification of fractions parenthesis can also be used. The three parenthesis (1st), {2nd}, [3rd] are used commonly.
Examples on simplification of fractions:
1. 3 1/3 ÷ 5/3 - 1/10 of 2 ½ + 7/4
Solution:
3 1/3 ÷ 5/3 - 1/10 of 2 ½ + 7/4
= (3 × 3 + 1)/3 ÷ 5/3 – 1/10 of (2 × 2 + 1)/2 + 7/4
= 10/3 ÷ 5/3 - 1/10 of 5/2 + 7/4
[‘of’ simplified]
= 10/3 × 3/5 – ½ × ½ + 7/4 [‘÷’ simplified]
= 2/1 - ¼ + 7/4 [‘×’ simplified]
= (2 × 4)/(1 × 4) - (1 × 1)/(4 × 1) + (7 × 1)/(4 × 1)
= 8/4 - ¼ + 7/4
[Now the denominators are same of all the fractions]
= (8 – 1 + 7)/4 [‘+’ and ‘-‘ simplified]
= 14/4
= 7/2
= 3\(\frac{1}{2}\)
2. 45 of 3/5 ÷ 1 2/3 + 3 of 1/3 – 10
Solution:
45 of 3/5 ÷ 1 2/3 + 3 of 1/3 – 10
= 45 of 3/5 ÷ (1 × 3 + 2)/3 + 3 of 1/3 – 10
= 45 of 3/5 ÷ 5/3 + 3 of 1/3 – 10
= 45 × 3/5 ÷ 5/3 + 3 × 1/3 – 10 [‘of’ simplified]
= 9 × 3 × 3/5 + 3 × 1/3 – 10 [‘÷’ simplified], [‘×’ simplified]
= (27 × 3)/5 + 1 – 10
= 81/5 + 1 – 10
= (81 × 1)/(5 × 1) + (1 × 5)/(1 × 5) – (10 × 5)/(1 × 5)
= 81/5 + 5/5 – 50/5
[Now the denominators are same of all the fractions]
= (81 + 5 – 50)/5 [‘+’ and ‘-‘ simplified]
= 36/5
= 7 1/5
43 of 1/86 ÷ 1/14 × 2/7 + 9/4 – ¼
Solution:
43 of 1/86 ÷ 1/14 × 2/7 + 9/4 – ¼
= 43 × 1/86 ÷ 1/14 × 2/7 + 9/4 – ¼
= 2/1 + 9/4 – ¼
= (2 × 4)/(1 × 4) + (9 × 1)/(4 × 1) - (1 × 1)/(4 × 1)
= 8/4 + 9/4 - 1/4
[Now the denominators are same of all the fractions]
= (8 + 9 - 1)/4
= 16/4
= 4
4. 9/10 ÷ (3/5 + 2 1/10)
Solution:
9/10 ÷ (3/5 + 2 1/10)
= 9/10 ÷ (3/5 + 21/10)
= 9/10 ÷ ((6 +21)/10)
[Solve within brackets]
= 9/10 ÷ 27/10
= 9/10 × 10/27
= 1/3
5. (7 ¼ - 6 1/4) of (2/5 + 3/15)
Solution:
(7 ¼ - 6 1/4) of (2/5 + 3/15)
= (29/4 – 25/4) of (2/5 + 3/15)
= ((29 – 25)/4) × ((6 + 3)/15)
[Solve within brackets]
= 4/4 × 9/15
[Reduce to lowest term]
= 1 × 3/5
= 3/5
6. {18 + (2 ½ + 4/5)} of 1/1000
Solution:
{18 + (2 ½ + 4/5)} of 1/1000
= {18 + (5/2 + 4/5)} of 1/1000
= {18 + ((25 + 8)/10)} of 1/1000
= {18 + 33/10} of 1/1000
= {(180 + 33)/10} of 1/1000
= 213/10 of 1/1000
= 213/10 × 1/1000
= (213 × 1)/(10 × 1000)
= 213/10000
= 0.0213
These are the examples of simplification of fractions.
● Multiplication is Repeated Addition.
● Multiplication of Fractional Number by a Whole Number.
● Multiplication of a Fraction by Fraction.
● Properties of Multiplication of Fractional Numbers.
● Worksheet on Multiplication on Fraction.
● Division of a Fraction by a Whole Number.
● Division of a Fractional Number.
● Division of a Whole Number by a Fraction.
● Properties of Fractional Division.
● Worksheet on Division of Fractions.
● Simplification of Fractions.
● Worksheet on Simplification of Fractions.
● Worksheet on Word Problems on Fractions.
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5th Grade Math Problems
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