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Question

Which of the following statements are true:

(i) 10 ÷ (5 × 2) = (10 ÷ 5) × (10 ÷ 2)
(ii) (35 − 14) ÷ 7 = 35 ÷ 7 − 14 ÷ 7
(iii) 35 − 14 ÷ 7 = 35 ÷ 7 − 14 ÷ 7
(iv) (20 − 5) ÷ 5 = 20 ÷ 5 − 5
(v) 12 × (14 ÷ 7) = (12 × 14) ÷ (12 × 7)
(vi) (20 ÷ 5) ÷ 2 = (20 ÷ 2) ÷ 5

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Solution

(i) False
LHS: 10 ÷ (5 × 2)
= 10 ÷ 10
= 1
RHS: (10 ÷ 5) × (10 ÷ 2)
= 2 × 5
= 10

(ii) True
LHS: (35 − 14) ÷ 7
= 21 ÷ 7
= 3
RHS: 35 ÷ 7 − 14 ÷ 7
= 5 − 2
= 3

(iii) False
LHS: 35 − 14 ÷ 7
= 35 − 2
= 33
RHS: 35 ÷ 7 − 14 ÷ 7
= 5 − 2
= 3

(iv) False
LHS: (20 − 5) ÷ 5
= 15 ÷ 5
= 3
RHS: 20 ÷ 5 − 5
= 4 − 5
= −1

(v) False
LHS: 12 × (14 ÷ 7)
= 12 × 2
= 24
RHS: (12 × 14) ÷ (12 × 7)
= 168 ÷ 84
= 2

(vi) True
LHS: (20 ÷ 5) ÷ 2
= 4 ÷ 2
= 2
RHS: (20 ÷ 2) ÷ 5
= 10 ÷ 5
= 2

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