balancing the equations Practice Questions Answers Test with Solutions & More Shortcuts

mathematical operations PRACTICE TEST [2 - EXERCISES]

symbol substitution

balancing the equations

Question : 1 [S.S.C (Steno) 2013]

Which of the following sets of operation with the usual notations replacing the stars in the order given makes the statements valid?

$√{100} * √{16} * √{225} * √{1}$

a) x, =, +

b) +, =, -

c) +, =, x

d) -, x, =

Answer: (b)

$√{100} + √{16} = √{225} - √{1}$

10+ 4 = 15 -1

⇒ 14 = 14

Question : 2 [S.S.C (Multitasking) 2014]

Select the correct combination of mathematical signs to replace * signs and to balance the following equation

8 * 8 * 1 *  7 = 8

a) x ÷ +

b) + ÷ x

c) ÷  x +

d) + x  ÷

Answer: (c)

From option (c),

8 * 8 * 1 * 7 = 8

⇒  8 ÷ 8 x 1+7=8

⇒ 8= 8

Question : 3 [S.S.C (10+2) 2013]

Select the correct combination of mathematical signs to replace ‘*’ signs and to balance the given equation.

24 * 34 * 2 * 5 * 12

a) + ÷ x =

b) = ÷ + -

c) = ÷ - +

d) + ÷ = x

Answer: (c)

From option (c).

24 = 34 ÷ 2 - 5+ 12

⇒ 24 = 17 - 5+12

⇒ 24 = 29 -5

⇒ 24 = 24

Question : 4 [S.S.C (CPO) 2013]

Select the correct combination of mathematical signs to replace the * signs and to balance the given equation

40 * 2 * 4 * 3 * 8

a) + - ÷= 

b) ÷ + = x 

c) + ÷ x =

d) + x - = 

Answer: (b)

Given, 40* 2* 4 * 3 * 8

Let us check all the options one by one.

From option (a), putting the signs in given equation, we get

40 + 2 - 4 ÷ 3 = 8

⇒ 42 - $4/3$ = 8

⇒ 126 - 4 = 24

⇒ 122 = 24

∴ LHS ≠ RHS

So, option (a) is incorrect.

From option (b), putting the signs in given equation, we get

40 ÷ 2 + 4 = 3 x 8

⇒  20 + 4 = 24

⇒ 24 = 24

LHS = RHS

Hence, option (b) is correct and there is no need to check remaining options.

Directions:

What should be the correct signs to balance the following equation?

Question : 5

17 - 3 x 6 = 45

a) x,-and =

b) =, x and –

c) -, x and =

d) x, = and -

Answer: (a)

From option (a),

17 - 3 x 6 = 45

By interchanging the signs, from the options. We get,

⇒ 17 x 3 - 6 = 45 (using VBODMAS rule)

⇒  51- 6 = 45

⇒  45 = 45

LHS = RHS

∴ So, option (a) is correct.

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