# Numbers and Operations Worksheets

Numbers and Operations Worksheets
• Page 1
1.
Use the symbol < or > or =, to show the relationship between - 7, - $\sqrt{64}$
 a. - 7 > - 8 b. - 7 < - 8 c. - 7 = - 8

#### Solution:

We know - 64 = - 8

So, - 7 > - 8

2.
Name the property of the statement: - 11 + 11 = 0
 a. Identity property of addition b. Closure property of addition c. Inverse property of addition d. None of these

#### Solution:

For every real number a, there is a unique additive inverse - a, such that a + (- a) = 0 and (- a) + a = 0

So, it is the inverse property of addition.

3.
Determine whether the associative property satisfied under the division operation.
 a. No b. Yes

#### Solution:

(a ÷ b) ÷ c = abc1 = abc

a ÷ (b ÷ c) = abc = acb

abcacb

So, (a ÷ b) ÷ ca ÷ (b ÷ c)

Associative property is not satisfied under the division operation.

4.
Name the property of the statement: 17 · (14 · 9) = (17 · 14) · 9
 a. Associative property of multiplication b. Commutative property of multiplication c. Distributive property of multiplication d. Closure property of multiplication

#### Solution:

a · (b · c) = (a · b) · c for all real numbers a, b and c, indicates the associative property of multiplication.

5.
If a scooter travels 216 km on 6 liters of petrol, how many kilometers will it travel on 10 liters of petrol?
 a. 324 km b. 360 km c. 288 km d. 396 km

#### Solution:

On 6 liters of petrol, the scooter travels 216 km.

On 1 liter of petrol, it travels 216 / 6 km

On 10 liters of petrol, it travels 216 / 6 × 10 km

= 36 × 10 km

= 360 km

6.
Find the additive inverse of .
 a. $\frac{3}{2}$ b. $\frac{2}{3}$ c. - $\frac{3}{2}$ d. - $\frac{2}{3}$

#### Solution:

2- 3 = - 23

For every real number Ã¢â‚¬ËœxÃ¢â‚¬â„¢, there is unique additive inverse Ã¢â‚¬Ëœ- xÃ¢â‚¬â„¢.

So, additive inverse of 2- 3 is - ( - 23) = 23

7.
Find the multiplicative inverse of - $\frac{8}{7}$.
 a. $\frac{7}{8}$ b. $\frac{8}{7}$ c. - $\frac{7}{8}$ d. - $\frac{8}{7}$

#### Solution:

The multiplicative inverse of a non-zero real number is itÃ¢â‚¬â„¢s reciprocal.

The reciprocal of - 87 is - 78.

8.
Divide: - 12 ÷ (2)
 a. - 6 b. $\frac{1}{6}$ c. 5 d. - $\frac{1}{6}$

#### Solution:

To divide real numbers, multiply by the multiplicative inverse of the divisor.

- 12 ÷ 2

Multiplicative inverse of 2 is 1 / 2.

(- 12) ÷ 2 = (- 12) × 12 = - 6
[Simplify.]

9.
Divide: - 192 ÷ (- 12)
 a. - $\frac{1}{16}$ b. 16 c. $\frac{1}{16}$ d. - 12

#### Solution:

To divide real numbers, multiply by the multiplicative inverse of the divisor.

- 192 ÷ (- 12)

Multiplicative inverse of - 12 is - 1 / 12.

- 192 ÷ (- 12) = (- 192) × (- 1 / 12) = 16
[Simplify.]

10.
Simplify: 7 | 14 - 24 |
 a. - 90 b. 65 c. - 80 d. 70

#### Solution:

7 | 14 - 24 |

= 7 | 14 + (- 24) |