Worksheet: Properties of Addition of Rational Numbers

In this worksheet, we will practice using properties of addition in the set of rational numbers and determining the additive inverse.

Q1:

Find the additive inverse of 12.

  • A12
  • B12
  • C2
  • D2

Q2:

Which of the following is the sum 125125+125125?

  • Aa positive number
  • Ba negative number
  • Czero

Q3:

Evaluate 423+1313 using properties of addition.

  • A4
  • B912
  • C18
  • D823

Q4:

Find the additive inverse of 0.7.

Q5:

Find the additive inverse of 34.

Q6:

What is the additive identity in ?

Q7:

Find the additive inverse of 13.

  • A3
  • B13
  • C0
  • D3
  • E13

Q8:

Find the additive inverse of (20).

Q9:

What is the additive inverse of 37?

  • A1
  • B73
  • C37
  • D37
  • E73

Q10:

Find the additive inverse of 23.

  • A23
  • B23
  • C32
  • D32

Q11:

Find the additive inverse of 16.

  • A16
  • B16
  • C6
  • D6

Q12:

Evaluate 317+457 using properties of addition.

  • A1
  • B137
  • C767
  • D147

Q13:

Evaluate 879+1389 using properties of addition.

  • A229
  • B556
  • C2223
  • D519

Q14:

What property of addition states that the sum of any two rational numbers is always a rational number?

  • AThe commutative property
  • BThe associative property
  • CThe additive inverse property
  • DThe additive identity property
  • EThe closure property

Q15:

What property of addition is demonstrated by 29+49=49+29?

  • AThe additive inverse property
  • BThe associative property
  • CThe additive identity property
  • DThe commutative property
  • EThe closure property

Q16:

What property of addition is demonstrated by 12+0=12?

  • AThe additive inverse property
  • BThe closure property
  • CThe associative property
  • DThe additive identity property
  • EThe commutative property

Q17:

Which equation shows the associative property of addition?

  • A12+12=0
  • B12+23=23+12
  • C12+23=76
  • D12+23+34=12+23+34
  • E23+0=23

Q18:

Simplify 513+34+14 using the properties of addition.

  • A613
  • B921
  • C514
  • D1813
  • E917

Q19:

Evaluate 14+34+14.

  • A4
  • B34
  • C14
  • D1

Q20:

If 𝑎=1, 𝑏=2, 𝑐=3, and 𝑑=4, which of the following expressions does not result in a rational number?

  • A2𝑎𝑏𝑐+𝑑2𝑏𝑐
  • B𝑎+𝑏𝑐(𝑎+𝑏)+𝑐+𝑑𝑑
  • C𝑎𝑏+𝑏𝑑
  • D𝑎𝑏+𝑏𝑑+𝑎+𝑐
  • E𝑎+𝑏𝑏+𝑐+𝑑𝑑

Q21:

If 𝑎=1, 𝑏=5, 𝑐=3, and 𝑑=2, which of the following expressions does not result in a rational number?

  • A𝑎+𝑏𝑐(𝑑𝑏)+𝑐+𝑑𝑑
  • B𝑎+𝑏𝑏+𝑐+𝑑𝑑
  • C2𝑎𝑏𝑐+𝑑+𝑎+𝑑2𝑏𝑐
  • D2𝑎𝑏𝑐+𝑑2𝑏𝑐
  • E𝑎𝑏+𝑏𝑑

Q22:

If 𝑎=5, 𝑏=4, 𝑐=3, and 𝑑=2, which of the following expressions has a result that is not rational?

  • A𝑎+𝑏𝑎(𝑐+𝑑)+𝑐+𝑑𝑑
  • B(𝑏+𝑐)(𝑎+𝑑)𝑐+𝑏2𝑑𝑐
  • C𝑎+𝑏𝑏+𝑐+𝑑𝑑
  • D𝑏𝑎+(𝑐𝑎)𝑑
  • E𝑎𝑏+𝑏𝑑

Q23:

If 𝑎=3, 𝑏=2, 𝑐=6, and 𝑑=1, which of the following expressions has a result that is not rational?

  • A𝑎+𝑏𝑏+𝑐+𝑑𝑑
  • B(𝑎+𝑏+𝑑)𝑐+(𝑏+𝑐)𝑎
  • C2𝑎𝑏𝑐+𝑑2𝑏𝑐
  • D𝑎𝑏+𝑏𝑑
  • E𝑎+𝑏𝑎𝑏+𝑐+𝑐+𝑑𝑑

Q24:

Calculate the additive inverse of (10).

Q25:

Find the additive inverse of 165.

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