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.

  • A 2
  • B 2
  • C 1 2
  • D 1 2

Q2:

Which of the following is the sum 125125+125125?

  • Azero
  • B a negative number
  • C a positive number

Q3:

Evaluate 423+1313 using properties of addition.

  • A 9 1 2
  • B 8 2 3
  • C 18
  • D 4

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.

  • A 1 3
  • B 3
  • C 0
  • D 3
  • E 1 3

Q8:

Find the additive inverse of (20).

Q9:

What is the additive inverse of 37?

  • A 7 3
  • B 3 7
  • C 1
  • D 3 7
  • E 7 3

Q10:

Find the additive inverse of 23.

  • A 2 3
  • B 3 2
  • C 2 3
  • D 3 2

Q11:

Find the additive inverse of 16.

  • A 1 6
  • B 6
  • C 6
  • D 1 6

Q12:

Evaluate 317+457 using properties of addition.

  • A 7 6 7
  • B 1 3 7
  • C 1
  • D 1 4 7

Q13:

Evaluate 879+1389 using properties of addition.

  • A 2 2 2 3
  • B 5 1 9
  • C 2 2 9
  • D 5 5 6

Q14:

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

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

Q15:

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

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

Q16:

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

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

Q17:

Which equation shows the associative property of addition?

  • A 2 3 + 0 = 2 3
  • B 1 2 + 2 3 = 7 6
  • C 1 2 + 1 2 = 0
  • D 1 2 + 2 3 = 2 3 + 1 2
  • E 1 2 + 2 3 + 3 4 = 1 2 + 2 3 + 3 4

Q18:

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

  • A 9 2 1
  • B 6 1 3
  • C 5 1 4
  • D 9 1 7
  • E 1 8 1 3

Q19:

Evaluate 14+34+14.

  • A 4
  • B 3 4
  • C 1 4
  • D1

Q20:

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

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

Q21:

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

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

Q22:

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

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

Q23:

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

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

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