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]

= 0/4

= 0



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



3.

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.

Multiplicative Inverse.

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.

Word Problems on Fraction.

Worksheet on Word Problems on Fractions.





5th Grade Numbers Page

5th Grade Math Problems

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