Worksheet: Properties of Multiplication in a Set of Rational Numbers

In this worksheet, we will practice identifying the properties of the multiplication operation in the set of rational numbers.

Q1:

Which property of multiplication is used in 49×94=1?

  • AAssociative property
  • BClosure property
  • CMultiplicative-identity property
  • DMultiplicative-inverse property
  • ECommutative property

Q2:

Evaluate 25×15+25×25 using the properties of multiplication.

Q3:

Evaluate 9×47+47×17+16×47 using the properties of multiplication.

Q4:

Find the missing term in the equation 13×29=×13.

  • A 1 3
  • B 9 2
  • C3
  • D 2 9

Q5:

What is the multiplicative neutral element in ?

Q6:

Evaluate 1×12+12×9+8×12 using the properties of multiplication.

Q7:

Evaluate 9×12+12×17+16×12 using the properties of multiplication.

Q8:

Which property of multiplication is used in 65×56=1?

  • AAssociative property
  • BClosure property
  • CMultiplicative-identity property
  • DMultiplicative-inverse property
  • ECommutative property

Q9:

Which property of multiplication is used in 817×178=1?

  • AAssociative property
  • BClosure property
  • CMultiplicative-identity property
  • DMultiplicative-inverse property
  • ECommutative property

Q10:

Which property of multiplication is used in 617×176=1?

  • AAssociative property
  • BClosure property
  • CMultiplicative-identity property
  • DMultiplicative-inverse property
  • ECommutative property

Q11:

Which property of multiplication is used in 38×83=1?

  • AAssociative property
  • BClosure property
  • CMultiplicative-identity property
  • DMultiplicative-inverse property
  • ECommutative property

Q12:

Which property of multiplication is used in 311×113=1?

  • AAssociative property
  • BClosure property
  • CMultiplicative-identity property
  • DMultiplicative-inverse property
  • ECommutative property

Q13:

Which property of multiplication is used in 32×23=1?

  • AAssociative property
  • BClosure property
  • CMultiplicative-identity property
  • DMultiplicative-inverse property
  • ECommutative property

Q14:

Which property of multiplication is used in 219×192=1?

  • AAssociative property
  • BClosure property
  • CMultiplicative-identity property
  • DMultiplicative-inverse property
  • ECommutative property

Q15:

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

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

Q16:

If 𝑎=1, 𝑏=2, 𝑐=3, and 𝑑=4, which of the following expressions results in a rational number?

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

Q17:

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 two rational numbers is rational. If 𝑎=7, 𝑏=3, 𝑐=0, and 𝑑=2, which of the following expressions results in a rational number?

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

Q18:

Which of the following equations illustrates the multiplicative inverse property?

  • A 𝑥 + ( 𝑏 + 𝑐 ) = ( 𝑥 + 𝑏 ) + 𝑐
  • B 𝑥 1 𝑥 = 1
  • C 𝑥 ( 𝑏 + 𝑐 ) = 𝑥 𝑏 + 𝑥 𝑐
  • D 𝑥 0 = 0
  • E 𝑥 + 𝑏 = 𝑏 + 𝑥

Q19:

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

Q20:

If 𝑎=3, 𝑏=2, 𝑐=4, and 𝑑=1, which of the following expressions results in a rational number?

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

Q21:

If 𝑎=9, 𝑏=7, 𝑐=0, and 𝑑=5, which of the following expressions has a result that is not rational?

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

Q22:

If 𝑎=6, 𝑏=3, 𝑐=5, and 𝑑=2, which of the following expressions has a result that is not rational?

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

Q23:

If 𝑎=3, 𝑏=2, 𝑐=4, and 𝑑=1, which of the following expressions results in a rational number?

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

Q24:

If 𝑎=1, 𝑏=2, 𝑐=3, and 𝑑=4, which of the following expressions results in a rational number?

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

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