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Worksheet: Applications of the Distributive Property

In this worksheet, we will practice applying the distributive property to evaluate expressions and solving problems including real-life situations.

Q1:

The average attendance per game during a season of baseball was about 65 000 people. Use the distributive property to find how many people attended 7 games during that season.

Q2:

Use the distributive property to calculate the value of 7 6 + 7 6 Γ— 2 5 βˆ’ 7 6 2 .

Q3:

Given that π‘₯ Γ— ( 6 + 9 ) = ( βˆ’ 7 Γ— 6 ) + ( βˆ’ 7 Γ— 9 ) , find the value of π‘₯ .

Q4:

Use the number bonds to help you find the missing numbers in the equations.

Q5:

Fill in the blank: 4 0 0 = ( 3 Γ— 1 0 0 ) + ( Γ— 1 0 0 ) .

Q6:

Isabella is trying to figure out the cost of 8 juice boxes that are sold for $4.11 each. Which of the following mathematical sentences can be used to help Isabella do her calculations easily and states the real number property applied?

  • A 8 ( 4 . 1 1 ) = 8 ( 4 + 0 . 1 1 ) , the commutative property of multiplication
  • B 8 ( 4 . 1 1 ) = 8 ( 4 + 0 . 1 1 ) , the associative property of multiplication
  • C 8 + 4 . 1 1 = 4 . 1 1 + 8 , the commutative property of addition
  • D 8 ( 4 . 1 1 ) = 8 ( 4 + 0 . 1 1 ) , the distributive property
  • E 8 + 4 . 1 1 = 8 + ( 4 + 0 . 1 1 ) , the distributive property

Q7:

Ethan bought 7 new outfits for $65 each for his wardrobe. Determine the expression that represents the total cost. Using the distributive property, determine an equivalent expression that can be used to calculate the total cost mentally.

  • A 7 Γ— 6 5 , 7 ( 6 0 βˆ’ 5 )
  • B 7 + 6 5 , 7 + ( 6 0 + 5 )
  • C 7 + 6 5 , 7 + ( 6 0 βˆ’ 5 )
  • D 7 Γ— 6 5 , 7 ( 6 0 + 5 )
  • E 7 Γ— 6 5 , 7 + ( 6 0 + 5 )

Q8:

Complete:

Q9:

Using the distributive property, calculate 5 9 + 5 9 Γ— ( βˆ’ 4 9 ) 2 .

Q10:

Complete:

Q11:

Use Matthew’s fact to find the missing numbers.

2 2 Γ— 1 2 = 1 3 2 +

2 2 Γ— 1 2 =

Q12:

A print shop charges $0.04 to print a page in black and white and $0.16 to print it in color. Use the distributive property to determine the total cost of printing 27 pages in both black and white and color.

Q13:

A hardware store has 154 hammers and 171 screwdrivers on sale for $9.03 each. Determine how much money the hardware store will earn if all the hammers and screwdrivers are sold. If the selling price decreased to $6.69, determine how much money the store would earn then, and calculate the difference between the store’s earnings for both prices.

  • A$1 561.62, $1 201.26, $360.36
  • B$334.03, $331.69, $665.72
  • C$1 698.13, $1 297.99, $400.14
  • D$2 934.75, $2 174.25, $760.50
  • E$2 934.75, $2 174.25, $5 109.00

Q14:

Using the distributive property, calculate 1 2 + 1 2 Γ— 8 8 2 .

Q15:

Using the distributive property, calculate 5 7 Γ— 4 7 βˆ’ 4 7 2 .

Q16:

Evaluate and simplify 3 8 Γ— 9 1 6 + 5 1 6 Γ— 1 2 + 3 8 Γ— 1 8 + 5 1 6 Γ— ο€Ό βˆ’ 1 8  properties of real numbers.

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

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