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.

  • A13
  • B92
  • C3
  • D29

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?

  • A2𝑎𝑏𝑐×𝑑2𝑏𝑐
  • B𝑎𝑏𝑏×𝑐+𝑑𝑐𝑑
  • C𝑎+𝑏𝑏×𝑐+𝑑𝑑
  • D𝑎+𝑏𝑐(𝑑𝑏)×𝑐+𝑑𝑑
  • E𝑎𝑏×𝑏𝑑

Q16:

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

  • A𝑏𝑎×𝑑𝑐
  • B(𝑎+𝑏)𝑏×(𝑐+𝑑)𝑑
  • C𝑎𝑐×𝑏𝑐(𝑏+𝑎)
  • D𝑎𝑑(𝑎+𝑐)×𝑏𝑐
  • E(𝑎+𝑏𝑐)𝑏×(𝑎+𝑏+𝑐)𝑏2𝑎

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?

  • A𝑎𝑏×𝑐+𝑑𝑑
  • B𝑎+𝑏𝑐𝑑×𝑎𝑏𝑎+𝑏
  • C𝑎𝑐×𝑑𝑐
  • D𝑎𝑏×𝑑𝑐
  • E𝑎𝑐+𝑑×𝑑𝑐

Q18:

Which of the following equations illustrates the multiplicative inverse property?

  • A𝑥+(𝑏+𝑐)=(𝑥+𝑏)+𝑐
  • B𝑥1𝑥=1
  • C𝑥(𝑏+𝑐)=𝑥𝑏+𝑥𝑐
  • D𝑥0=0
  • E𝑥+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?

  • A𝑎𝑏𝑏×𝑐𝑑𝑑
  • B𝑎+𝑏𝑐(𝑎+𝑏)×𝑐+𝑑𝑑
  • C2𝑎𝑏𝑐×𝑑2𝑏𝑐
  • D𝑎𝑏×𝑏𝑑
  • E𝑎+𝑏𝑏×𝑐+𝑑𝑑

Q20:

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

  • A𝑎𝑎×𝑐𝑐
  • B𝑎+𝑏+𝑐𝑏+𝑎×𝑎+𝑏+𝑐2𝑑𝑏
  • C𝑎𝑑+(𝑐𝑎)×𝑏𝑐
  • D𝑎+𝑏𝑐𝑏×𝑎+𝑏+𝑐2𝑑𝑏
  • E𝑎+𝑏𝑏×𝑐+𝑑𝑑

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)×(𝑏2𝑑)(𝑎+𝑏)
  • B𝑎𝑏×𝑏𝑑
  • C𝑎𝑐𝑏×𝑐𝑑𝑎
  • D𝑎+𝑏2𝑏(𝑎+𝑑)×𝑐+𝑑𝑑
  • E𝑐𝑏×𝑎(𝑏2𝑑)

Q22:

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

  • A𝑎+𝑏𝑏𝑑𝑎×𝑐+𝑑𝑑
  • B𝑎+2𝑏𝑐×𝑑2𝑏𝑐
  • C(𝑎+𝑑)𝑏×𝑐(𝑏2𝑑)
  • D𝑎𝑏×𝑏𝑑
  • E𝑎+𝑏𝑏×𝑐+𝑑𝑑

Q23:

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

  • A𝑎𝑑+(𝑐𝑎)+𝑏𝑐
  • B𝑑𝑎+𝑏+𝑑+𝑏𝑐
  • C𝑎𝑎+𝑐𝑐
  • D𝑎+𝑏𝑏+𝑐+𝑑𝑑
  • E𝑎+𝑏𝑐𝑏+𝑎+𝑏+𝑐2𝑑𝑏

Q24:

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

  • A𝑎𝑑(𝑎+𝑐)+𝑏𝑐
  • B𝑏𝑎+𝑑𝑐
  • C𝑎+𝑏𝑐𝑏+𝑎+𝑏+𝑐𝑏2𝑎
  • D𝑏𝑑(𝑎+𝑐)+𝑑𝑐
  • E𝑎+𝑏𝑏+𝑐+𝑑𝑑

Q25:

Calculate the multiplicative inverse of 17.

  • A149
  • B49
  • C149
  • D49

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.