simplify 3/4+2/12+1/24-1/2
Answers
Answer:
(i) (1 / 2 + 1 / 3) ÷ (1 / 4 – 1 / 6)
The given expression can be simplified as follows
(1 / 2 + 1 / 3) ÷ (1 / 4 – 1 / 6) = [(3 + 2) / 6] ÷ [(3 – 2) / 12]
On further calculation, we get
= (5 / 6) ÷ (1 / 12)
= 5 / 6 × 12 / 1
= 5 × 2
= 10
Hence, the simplified form of the given expression is 10
(ii) (24 / 35 ÷ 6 / 7 + 5 / 9) × 3 / 4
The given expression can be simplified as follows
(24 / 35 ÷ 6 / 7 + 5 / 9) × 3 / 4 = (24 / 35 × 7 / 6 + 5 / 9) × 3 / 4
= (4 / 5 + 5 / 9) × 3 / 4
By taking LCM, we get
= [(36 + 25) / 45] × 3 / 4
= (61 / 45) × 3 / 4
We get
= 61 / 60
= 1
60
1
Hence, the simplified form of the given expression is
1
60
1
(iii) 3 / 4 of
6
8
1
– 2 / 3 of 2
4
1
The given expression can be simplified as below
3 / 4 of
6
8
1
– 2 / 3 of
2
4
1
= 3 / 4 of 49 / 8 – 2 / 3 of 9 / 4
= 3 / 4 × 49 / 8 – 2 / 3 of 9 / 4
= 147 / 32 – 2 / 3 × 9 / 4
We get
= 147 / 32 – 3 / 2
On taking LCM, we get
= [(147 – 48)] / 32
= 99 / 32
= 3
32
3
Hence, the simplified form of the given expression is
3
32
3
(iv) 7 / 30 of (1 / 3 + 7 / 15) ÷ (5 / 6 – 3 / 5)
The given expression can be simplified as below
7 / 30 of (1 / 3 + 7 / 15) ÷ (5 / 6 – 3 / 5) = 7 / 30 of [(5 + 7) / 15] ÷ [(25 – 18) / 30]
We get
= 7 / 30 of (4 / 5) ÷ (7 / 30)
= 7 / 30 × 4 / 5 × 30 / 7
= 4 / 5
Hence, the simplified form of the given expression is 4 / 5
(v)
2
2
1
−3
2
1
X1
4
3
+2
2
1
The given expression can be simplified as below
2
2
1
−3
2
1
X1
4
3
+2
2
1
= 5 / 2 – 7 / 2 × 7 / 4 + 5 / 2
= 5 / 2 – 49 / 8 + 5 / 2
= 5 / 2 + 5 / 2 – 49 / 8
By taking LCM, we get
= (20 + 20 – 49) / 8
= (40 – 49) / 8
= – 9 / 8
= -1
8
1
Hence, – 1
8
1
is the simplified form of the given expression
Step-by-step explanation:
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