Integers Test

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Integers Test - 25

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Weekly Quiz Competition

Question 1
1 / -0

Fill in the blank: $$27\times (23 + 27) = (27 \times 23) + (.....\times 27)$$

A
$$23$$

B
$$27$$

C
$$1$$

D
$$0$$

Solution

Distributive property states that,
$$a \times (b + c) = (a\times b) + (a\times c)$$
$$\therefore 27 \times (23 + 27) = (23 \times 27) + (27\times 27)$$.
Question 2
1 / -0

Simplify using associative property:
$$(-5) \times [(-8) \times 2] =$$ $$....$$

A
$$40$$

B
$$-80$$

C
$$80$$

D
$$-40$$

Solution

$$(-5) \times [(-8)\times 2] = (-5)\times (2\times (-8))$$ (commutative property)
$$= [(-5)\times 2] \times (-8)$$ (associative property)
$$= (-10) \times (-8)$$
$$= 80$$
(Here, we used various properties to skip $$(-5)\times (-8)$$ which could have been time consuming).
Question 3
1 / -0

The value of $$4 + (3 + (-7)) $$ is

A
$$1$$

B
$$-1$$

C
$$0$$

D
$$-14$$

Solution

$$4 + (3 + (-7)) = (4 + 3) + (-7)$$ (associative property)
$$= 7 + (-7)$$
$$= 0$$
Question 4
1 / -0

Fill in the blank :
$$3\times [(-6) + .....] = 3\times (-6) + 3\times 8$$

A
$$8$$

B
$$(-8)$$

C
$$3$$

D
$$(-6)$$

Solution

$$a\times (b + c) = a\times b + a\times c$$
is the distributive property over addition for integers.
$$\therefore 3\times (-6) + 3\times 8 = 3\times [(-6) + 8]$$.
Question 5
1 / -0

The value of $$[(5 + (-13) )+ 5]$$ is

A
$$-3$$

B
$$3$$

C
$$-13$$

D
$$10$$

Solution

$$5 + (-13) + 5 = 5 + 5 + (-13)$$ (commutative property)
$$= (5 + 5) + (-13)$$ (associative property)
$$= 10 + (-13)$$
$$= -3$$
Question 6
1 / -0

The value of $$[28\times (-5)] \times 4 $$ is

A
$$270$$

B
$$-270$$

C
$$-560$$

D
$$560$$

Solution

$$[28 \times (-5)]\times 4 =28\times [(-5) \times 4]$$ (associative property)
$$= 28\times (-20)$$
$$= -560$$.
Question 7
1 / -0

Find the missing value: $$[12 + (-4)] + ...... = 12 + [.... + 3]$$

A
$$-4, 3$$

B
$$3, -4$$

C
$$3, 4$$

D
$$-5, 5$$

Solution

Addition is associative for integers.
$$i.e. (a + b) + c = a + (b + c)$$
$$\therefore [12 + (-4)] + 3 = 12 + [(-4) + 3]$$
$$\therefore$$ The missing terms are $$3, -4.$$
Question 8
1 / -0

Which of the following shows the distributive property of multiplication over subtraction?

A
$$x (y - z) = (x\times y) - (x\times z)$$

B
$$x (y - z) = (x\times y) - z$$

C
$$x \times (-y) = (-x) \times y$$

D
$$x\times \left (\dfrac {-1}{y}\right ) = (-x) \times \left (\dfrac {1}{y}\right )$$

Solution

$$x (y - z) = (x\times y) - (x\times z)$$ shows the distributive property of multiplication over subtraction.
Question 9
1 / -0

Find the value of following:
$$-7-(-8)$$

A
$$15$$

B
$$-15$$

C
$$1$$

D
$$-1$$

Solution

Given that
We have to find the value of given expression

$$-7-(-8)$$

we know that $$(-) \times (-) = +$$

and $$(+) \times (-) = -$$

$$=-7+8$$

$$=1$$
So option $$C $$ is correct
Question 10
1 / -0

Fill in the blank :
$$.....\times [4 + (-2)] = (-19) \times 4 + (-19) \times (-2)$$

A
$$(-2)$$

B
$$4$$

C
$$19$$

D
$$(-19)$$

Solution

$$(a\times b) + (a\times c) = a\times (b + c)$$ is the distributive property over addition for integers.
$$\therefore (-19) \times 4 + (-19) \times (-2) = (-19) \times [4 + (-2)]$$.

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Re-Attempt Weekly Quiz Competition

Integers Test - 25

Result

Integers Test - 25

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Rank

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SHARING IS CARING

Question 1

$$23$$

$$27$$

$$1$$

$$0$$

Solution

Question 2

$$40$$

$$-80$$

$$80$$

$$-40$$

Solution

Question 3

$$1$$

$$-1$$

$$0$$

$$-14$$

Solution

Question 4

$$8$$

$$(-8)$$

$$3$$

$$(-6)$$

Solution

Question 5

$$-3$$

$$3$$

$$-13$$

$$10$$

Solution

Question 6

$$270$$

$$-270$$

$$-560$$

$$560$$

Solution

Question 7

$$-4, 3$$

$$3, -4$$

$$3, 4$$

$$-5, 5$$

Solution

Question 8

$$x (y - z) = (x\times y) - (x\times z)$$

$$x (y - z) = (x\times y) - z$$

$$x \times (-y) = (-x) \times y$$

$$x\times \left (\dfrac {-1}{y}\right ) = (-x) \times \left (\dfrac {1}{y}\right )$$

Solution

Question 9

$$15$$

$$-15$$

$$1$$

$$-1$$

Solution

Question 10

$$(-2)$$

$$4$$

$$19$$

$$(-19)$$

Solution

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