# 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

**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.