Worksheet: Operations on Real Numbers

In this worksheet, we will practice solving problems involving operations and properties of operations on real numbers.

Q1:

Complete 3 + 1 2 = 1 2 + .

  • A 3
  • B 3
  • C 1 5
  • D 1 5

Q2:

Find the multiplicative inverse of 6 + 7 expressing your answer in simplest form.

  • A 1 7 6
  • B 1 6 7
  • C 6 7
  • D 7 6

Q3:

Given that the dimensions of a rectangle are 1 2 + 2 cm and 1 2 2 cm, find its area.

Q4:

What is the additive inverse of 9 1 1 7 ?

  • A 1 7 1 7 9 1
  • B 9 1 1 7 1 7
  • C 1 7 1 7 9 1
  • D 9 1 1 7 1 7

Q5:

Find the additive inverse of 8 1 3 5 .

  • A 8 + 1 3 5
  • B 1 3 5 8
  • C 1 3 5 8
  • D 1 8 1 3 5

Q6:

Find the multiplicative inverse of 6 3 0 .

  • A 5 6
  • B 5 6
  • C 6 3 0
  • D 3 0 6
  • E 3 0 6

Q7:

Given that 𝑎 3 is the multiplicative inverse of 1 3 , find the value of 𝑎 .

Q8:

Given that 𝑎 5 is the multiplicative inverse of 5 1 1 , find the value of 𝑎 .

  • A 1 1 5
  • B 5 1 1
  • C 5
  • D 1 1 5
  • E 1 1 5

Q9:

Given that the multiplicative inverse of 𝑎 + 2 is 𝑎 2 1 0 , find the value of 𝑎 .

Q10:

Given that 𝑥 = 1 1 2 8 , find 𝑥 .

  • A 1 4 1 4
  • B 8 1 4
  • C 2 2
  • D 1 4
  • E 2 4

Q11:

What is the additive inverse of 6 5 8 5 ?

  • A 8 5 6 5
  • B 6 5 8 5
  • C 8 5 6 5
  • D 6 5 + 8 5

Q12:

Find the multiplicative inverse of 0 . 3 6 , giving your answer in its simplest form.

  • A 5 6
  • B 3 5
  • C 5 3
  • D 1 3
  • E 1 2

Q13:

Find the multiplicative inverse of 1 2 1 4 .

  • A 1 4 1 2
  • B 1 4 1 2
  • C 1 2 1 4
  • D 1 2 1 4

Q14:

Complete 2 + 1 3 = 1 3 + .

  • A 2
  • B 1 5
  • C 2
  • D 1 5

Q15:

Find the volume of the cube, given that the length of its edge is 1 1 0 1 2 cm.

  • A 12 cm3
  • B 3 2 5 0 cm3
  • C 22 cm3
  • D 6 5 cm3

Q16:

Given that the dimensions of a rectangle are 5 7 + 7 2 cm and 5 7 7 2 cm, find the length of its perimeter.

Q17:

A square has a side length of 𝑙 cm and an area of 63 cm2. Find the area of a square whose side length is 6 𝑙 cm.

  • A 378 cm2
  • B 2,268 cm2
  • C 1 0 8 7 cm2
  • D 1 8 7 cm2
  • E 99 cm2

Q18:

The radius 𝑟 of a sphere is given by the formula 𝑟 = 3 𝑉 4 𝜋 , where 𝑉 is the sphere’s volume. Determine the difference in radius between a sphere with volume 3 6 𝜋 and a sphere with 2 , 3 0 4 𝜋 .

Q19:

A rational number is a number that can be written in the form 𝑎 𝑏 , where 𝑎 and 𝑏 are integers (whole numbers) and 𝑏 is not zero. If we add an irrational number to a rational number, the result is irrational. If 𝑎 = 2 , 𝑏 = 6 , 𝑐 = 2 , and 𝑑 = 1 , which of the following expressions results in a rational number?

  • A 𝑎 𝑐 + 𝑑 𝑐
  • B 𝑎 𝑏 + 𝑐 2 𝑐
  • C 𝑎 + 𝑏 𝑐 𝑑 + 𝑎 𝑏 𝑎 + 𝑏
  • D 𝑎 𝑏 ( 2 𝑎 + 2 𝑑 ) + 𝑑 𝑏
  • E 𝑎 𝑏 + 𝑑 𝑐

Q20:

A rational number is a number that can be written in the form 𝑎 𝑏 , where 𝑎 and 𝑏 are integers (whole numbers) and 𝑏 is not zero. The product of an irrational number and a nonzero rational number is an irrational number. If 𝑎 = 2 , 𝑏 = 6 , 𝑐 = 2 , and 𝑑 = 1 , which of the following expressions results in a rational number?

  • A 𝑎 𝑐 ( 𝑎 + 𝑑 ) × 𝑑 𝑐
  • B 𝑎 𝑏 × 𝑑 𝑐
  • C 𝑐 𝑏 × 𝑎 𝑏 2 𝑐
  • D 𝑎 + 𝑏 𝑐 𝑑 × 𝑎 𝑏 𝑎 + 𝑏
  • E 𝑎 𝑐 × 𝑐 𝑑

Q21:

If 𝑎 = 6 , 𝑏 = 8 , 𝑐 = 2 , and 𝑑 = 2 , which of the following expressions results in a rational number?

  • A 𝑏 𝑎 × 𝑑 𝑐
  • B 𝑐 𝑎 × 𝑎 ( 𝑏 4 𝑑 )
  • C 𝑐 + 𝑑 𝑎 𝑏 × 𝑎 + 𝑏 + 𝑐 𝑎 2 𝑐
  • D 𝑎 𝑎 ( 𝑏 𝑑 ) × 𝑏 𝑐
  • E 𝑎 + 𝑏 𝑐 × 𝑐 + 𝑐 𝑑 𝑑

Q22:

If 𝑎 = 2 , 𝑏 = 5 , 𝑐 = 2 , and 𝑑 = 3 , which of the following expressions results in a rational number?

  • A 𝑎 + 𝑏 𝑏 + 𝑐 + 𝑑 𝑐 𝑑 𝑏
  • B 𝑎 𝑑 ( 𝑎 + 𝑏 ) + 𝑏 𝑐
  • C 𝑎 𝑑 + 𝑎 ( 𝑐 2 𝑎 )
  • D 𝑎 + 𝑏 𝑐 𝑏 + 𝑎 + 𝑏 + 𝑐 𝑎 + 𝑏 𝑑
  • E 𝑎 𝑎 + 𝑐 𝑐

Q23:

If 𝑎 = 5 , 𝑏 = 4 , 𝑐 = 2 , and 𝑑 = 2 , which of the following expressions results in a rational number?

  • A 𝑏 𝑎 + 𝑑 𝑐
  • B 𝑐 𝑏 + 𝑎 𝑏 2 𝑑
  • C 𝑎 𝑑 ( 𝑎 𝑐 ) + 𝑏 𝑐
  • D 𝑐 + 𝑑 𝑎 𝑏 + 𝑎 + 𝑏 + 𝑐 𝑏 2 𝑑
  • E 𝑎 + 𝑏 𝑏 + 𝑐 + 𝑑 𝑐 𝑑

Q24:

If 𝑎 = 2 , 𝑏 = 1 0 , 𝑐 = 8 , and 𝑑 = 6 , which of the following expressions results in a rational number?

  • A 𝑎 + 2 𝑎 𝑏 𝑐 × 𝑐 + 𝑐 𝑑 𝑎
  • B 𝑐 𝑏 × 𝑑 ( 𝑐 2 𝑎 )
  • C 𝑎 + 𝑏 𝑐 𝑏 × 𝑎 + 𝑏 + 𝑐 𝑎 + 𝑏 𝑑
  • D 𝑐 𝑎 × 𝑎 𝑐
  • E 𝑎 𝑑 ( 𝑎 + 𝑏 ) × 𝑏 𝑐

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