Question : Directions: By Interchanging which two signs the equation will be correct?
27 ÷ 3 – 18 + 3 × 2 = 18
Option 1: + and –
Option 2: × and +
Option 3: + and ÷
Option 4: ÷ and ×
Correct Answer: + and ÷
Solution :
Given:
27 ÷ 3 – 18 + 3 × 2 = 18
Let's check the given options –
First option:
+ and –
On interchanging the mathematical signs, we get –
27 ÷ 3 + 18 – 3 × 2 = 18
Solving the L.H.S. of the given equation –
= 27 ÷ 3 + 18 – 3 × 2
=
9 + 18 – 3 × 2
=
9 + 18 – 6
= 21 ≠ 18
Second option:
× and +
On interchanging the mathematical signs, we get –
27 ÷ 3 – 18 × 3 + 2 = 18
Solving the L.H.S. of the given equation –
= 27 ÷ 3 – 18 × 3 + 2
= 9 – 18 × 3 + 2
= 9 – 54 + 2
= –43 ≠ 18
Third option:
+ and ÷
On interchanging the mathematical signs, we get –
27 + 3 – 18 ÷ 3 × 2 = 18
Solving the L.H.S. of the given equation –
= 27 + 3 – 18 ÷ 3 × 2
= 27 + 3 – 6 × 2
= 27 + 3 – 12
= 18 = R.H.S.
Fourth option:
÷ and ×
On interchanging the mathematical signs, we get –
27 × 3 – 18 + 3 ÷ 2 = 18
Solving the L.H.S. of the given equation –
= 27 × 3 – 18 + 3 ÷ 2
= 27 × 3 – 18 + 1.5
= 81 – 18 + 1.5
= 64.5 ≠ 18
So, only the third option satisfies the R.H.S. of the equation. Hence, the third option is correct.
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