Simplify 2/3^-6*2/3^-3 divided by 4/9^2
Answers
Step-by-step explanation:
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. 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
Answer:
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