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+12=12+.

  • A3
  • B3
  • C15
  • D15

Q2:

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

  • A167
  • B176
  • C76
  • D67

Q3:

Given that the dimensions of a rectangle are 12+2 cm and 122 cm, find its area.

Q4:

What is the additive inverse of 9117?

  • A171791
  • B171791
  • C911717
  • D911717

Q5:

Find the additive inverse of 8135.

  • A1358
  • B8+135
  • C1358
  • D18135

Q6:

Find the multiplicative inverse of 630.

  • A56
  • B306
  • C56
  • D306
  • E630

Q7:

Given that 𝑎3 is the multiplicative inverse of 13, find the value of 𝑎.

Q8:

Given that 𝑎5 is the multiplicative inverse of 511, find the value of 𝑎.

  • A115
  • B115
  • C511
  • D115
  • E5

Q9:

Given that the multiplicative inverse of 𝑎+2 is 𝑎210, find the value of 𝑎.

Q10:

Given that 𝑥=1128, find 𝑥.

  • A1414
  • B14
  • C24
  • D814
  • E22

Q11:

What is the additive inverse of 6585?

  • A65+85
  • B6585
  • C8565
  • D8565

Q12:

Find the multiplicative inverse of 0.36, giving your answer in its simplest form.

  • A53
  • B12
  • C13
  • D56
  • E35

Q13:

Find the multiplicative inverse of 1214.

  • A1412
  • B1214
  • C1412
  • D1214

Q14:

Complete 2+13=13+.

  • A2
  • B2
  • C15
  • D15

Q15:

Find the volume of the cube, given that the length of its edge is 11012 cm.

  • A22 cm3
  • B12 cm3
  • C65 cm3
  • D3250 cm3

Q16:

Given that the dimensions of a rectangle are 57+72 cm and 5772 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 6𝑙 cm.

Q18:

The radius 𝑟 of a sphere is given by the formula 𝑟=3𝑉4𝜋, where 𝑉 is the sphere’s volume. Determine the difference in radius between a sphere with volume 36𝜋 and a sphere with 2,304𝜋.

Q19:

A rational number is a number that can be written in the form 𝑎𝑏, 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?

  • A𝑎𝑐+𝑑𝑐
  • B𝑎𝑏(2𝑎+2𝑑)+𝑑𝑏
  • C𝑎𝑏+𝑐2𝑐
  • D𝑎+𝑏𝑐𝑑+𝑎𝑏𝑎+𝑏
  • E𝑎𝑏+𝑑𝑐

Q20:

A rational number is a number that can be written in the form 𝑎𝑏, 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?

  • A𝑎𝑏×𝑑𝑐
  • B𝑐𝑏×𝑎𝑏2𝑐
  • C𝑎𝑐×𝑐𝑑
  • D𝑎+𝑏𝑐𝑑×𝑎𝑏𝑎+𝑏
  • E𝑎𝑐(𝑎+𝑑)×𝑑𝑐

Q21:

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

  • A𝑎+𝑏𝑐×𝑐+𝑐𝑑𝑑
  • B𝑎𝑎(𝑏𝑑)×𝑏𝑐
  • C𝑐𝑎×𝑎(𝑏4𝑑)
  • D𝑏𝑎×𝑑𝑐
  • E𝑐+𝑑𝑎𝑏×𝑎+𝑏+𝑐𝑎2𝑐

Q22:

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

  • A𝑎+𝑏𝑐𝑏+𝑎+𝑏+𝑐𝑎+𝑏𝑑
  • B𝑎𝑎+𝑐𝑐
  • C𝑎+𝑏𝑏+𝑐+𝑑𝑐𝑑𝑏
  • D𝑎𝑑+𝑎(𝑐2𝑎)
  • E𝑎𝑑(𝑎+𝑏)+𝑏𝑐

Q23:

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

  • A𝑏𝑎+𝑑𝑐
  • B𝑎𝑑(𝑎𝑐)+𝑏𝑐
  • C𝑐𝑏+𝑎𝑏2𝑑
  • D𝑎+𝑏𝑏+𝑐+𝑑𝑐𝑑
  • E𝑐+𝑑𝑎𝑏+𝑎+𝑏+𝑐𝑏2𝑑

Q24:

If 𝑎=2, 𝑏=10, 𝑐=8, and 𝑑=6, which of the following expressions results in a rational number?

  • A𝑐𝑏×𝑑(𝑐2𝑎)
  • B𝑎+2𝑎𝑏𝑐×𝑐+𝑐𝑑𝑎
  • C𝑎+𝑏𝑐𝑏×𝑎+𝑏+𝑐𝑎+𝑏𝑑
  • D𝑐𝑎×𝑎𝑐
  • E𝑎𝑑(𝑎+𝑏)×𝑏𝑐

Q25:

If 𝑥=523 and 𝑦=16, is it true that 2𝑥+𝑦=1?

  • Ano
  • Byes

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