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Worksheet: Multiplication and Division Equations

Q1:

Fish A is 2 times as long as fish B. Write an equation to determine the length of fish B if fish A is 6 meters long, and then solve it.

  • A 4 π‘₯ = 2 , 2
  • B 6 π‘₯ = 2 , 3
  • C 2 π‘₯ = 4 , 2
  • D 2 π‘₯ = 6 , 3
  • E 8 π‘₯ = 2 , 4

Q2:

Which of the following equations does NOT belong with the others?

  • A 1 0 π‘₯ = 6 0
  • B 4 π‘₯ = 2 4
  • C 3 π‘₯ = 1 8
  • D 1 2 π‘₯ = 2 4

Q3:

Solve π‘₯ 6 . 5 = 5 . 5 .

Q4:

Solve for π‘₯ 2 9 π‘₯ = 1 3 : .

  • A π‘₯ = 5 9
  • B π‘₯ = 2 3
  • C π‘₯ = 2 2 7
  • D π‘₯ = 1 1 2
  • E π‘₯ = 1 9

Q5:

The equation 5 𝑔 = 3 5 can be solved using the area model of multiplication as shown.

The next step to solve the equation is represented by the diagram.

Which of the following calculations is used to find the missing number?

  • A 3 5 + 5
  • B 3 5 Γ— 5
  • C 3 5 βˆ’ 5
  • D 3 5 Γ· 5
  • E 5 Γ· 3 5

Now we can use the following diagram to find the value of 𝑔 .

What is the value of 𝑔 ? ?

Q6:

A rectangle has an area of 9 1 6 square inches and a length of 6 1 3 inches. Solve the equation 9 1 6 = 6 1 3 Γ— 𝑀 to find the width 𝑀 of the rectangle.

  • A 𝑀 = 1 2
  • B 𝑀 = 3 8 5 5
  • C 𝑀 = 1 1 2
  • D 𝑀 = 1 1 7 3 8
  • E 𝑀 = 2 5 6

Q7:

Amelia paints one garden chair in 12 minutes. Write an equation for the number of chairs 𝑐 that she could paint in β„Ž hours.

  • A 𝑐 = 1 5 β„Ž
  • B 𝑐 = 1 2 β„Ž
  • C 𝑐 = 1 1 2 β„Ž
  • D 𝑐 = 5 β„Ž
  • E 𝑐 = 5 + β„Ž

Q8:

The equation 𝑔 = 2 𝑛 shows the relation between the number of cows, 𝑛 , that Matthew has and the number of bags of feed, 𝑔 , that he needs. If he needs 8 bags of feed, how many cows does he have?

Q9:

Determine whether the following statement is true or false: Whatever number you pick, if you multiply both sides of an equation by that number, the solution set remains the same.

  • Afalse
  • Btrue

Q10:

The equation 1 2 𝑝 = 𝑐 shows the total cost 𝑐 of a trip to the cinema in relation to the number of people 𝑝 that attend. If a trip cost $60, how many people attended?

Q11:

A plank of wood is 120 inches long. Knowing that there are 12 inches in 1 foot, solve the equation 1 2 𝑑 = 1 2 0 to find 𝑑 , the plank’s length in feet.

Q12:

Michael earns $8 per hour at his part-time job. Determine his new hourly rate after a raise of 3 . 5 % .

Q13:

If 𝑒 β‰  0 and π‘₯ 𝑒 = βˆ’ 1 , what is the value of π‘₯ ?

  • A 𝑒
  • B βˆ’ 1 𝑒
  • C βˆ’ 1
  • D βˆ’ 𝑒
  • E 1 𝑒

Q14:

In the equation 𝑝 = 2 𝑀 , the independent variable 𝑝 represents the total number of paintings that Olivia can make in 𝑀 weeks. After 6 weeks, how many paintings will Olivia have made?

Q15:

This piece of wrapping paper is too long.

Natalie wants to cut a piece which has an area of 40 cm2.

Write an equation that describes how to find the length of the piece. Use π‘₯ for the length.

  • A 8 + π‘₯ = 4 0
  • B π‘₯ = 8 Γ— 4 0
  • C π‘₯ βˆ’ 8 = 4 0
  • D 8 Γ— π‘₯ = 4 0

Q16:

Identify which of the list { 5 , 6 , 7 } is the solution of 5 0 = 1 0 π‘ž .

Q17:

The equation 𝑑 = 1 1 π‘š shows the time, 𝑑 , in minutes, that it takes Amelia to run π‘š miles. How many minutes does it take her to run 3 miles?

Q18:

The equation β„Ž = 4 𝑑 shows how the height, β„Ž , of a species of bamboo increases after 𝑑 days. Given that the height is measured in centimeters, how much height does the bamboo gain in 5 days?

Q19:

A rectangle’s width is one-sixth of its length. Given that the rectangle’s width is 9 inches, determine its length.

Q20:

The equation 𝑝 = 3 𝑔 represents the total number of golf balls 𝑔 that Daniel has in relation to the number of packets 𝑝 that he buys. If Daniel bought 3 new packets, how many golf balls would he have?

Q21:

The equation 𝑠 = 2 𝑏 shows the number of bags, 𝑏 , that Amelia buys in relation to the number of shoes, 𝑠 , that she buys. If Amelia bought 4 bags, how many shoes did she buy?

Q22:

I take a number and divide it by 3, and then divide by 6. The result is 2, what was the number?

Q23:

The currency in Switzerland is called a franc. On a certain day, one US dollar equaled 1 1 4 Swiss francs. Write and solve a multiplication equation to find the number of US dollars that would equal 25 Swiss francs.

  • A 2 5 = 1 1 4 Γ— 𝑛 , 𝑛 = 4 5
  • B 2 5 = 1 1 4 Γ— 𝑛 , 𝑛 = 5
  • C 1 1 4 = 2 5 Γ— 𝑛 , 𝑛 = 3 1
  • D 2 5 = 1 1 4 Γ— 𝑛 , 𝑛 = 2 0
  • E 𝑛 2 5 = 1 1 4 , 𝑛 = 5 0 0

Q24:

If 9 6 π‘₯ = 9 6 Γ— 5 5 , what is the value of π‘₯ ?

Q25:

Solve for π‘₯ : 2 1 = 1 1 2 π‘₯ .