Worksheet: One-step Equations: Multiplication and Division

In this worksheet, we will practice writing and solving one-step multiplication and division equations in questions including word problems.

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

Q2:

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

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

Q3:

Anthony bought five bars of chocolate of the same kind, each of the same price. If 𝑓 is the cost of each chocolate bar, solve 5𝑓=25 to determine 𝑓.

Q4:

It takes James 5 times longer than it takes Olivia to get to work. If James’s journey is 70 minutes, write an equation for the time (π‘₯) it takes Olivia to get to work. Then solve the equation.

  • A 7 0 π‘₯ = 5 , π‘₯ = 1 4
  • B 5 π‘₯ = 7 0 , π‘₯ = 1 4
  • C 6 5 π‘₯ = 5 , π‘₯ = 1 3
  • D 7 5 π‘₯ = 5 , π‘₯ = 1 5
  • E 5 π‘₯ = 6 5 , π‘₯ = 1 3

Q5:

Victoria has $112 and spends $14 each day. How long will it be until she has no money left?

Q6:

A car was traveling at a speed of 32 meters per second. At that rate, how long would it take for the car to cover a distance of 2,160 meters?

Q7:

Is the equation 36=3×𝑑 true or false if 𝑑=12?

  • Afalse
  • Btrue

Q8:

Jacob wants to buy a smartphone that costs $304. If he saves $38 each week, determine in how many weeks he will be able to buy the smartphone.

Q9:

Given that 1 gallon equals 4 quarts, write and solve an equation to find the number of gallons, π‘₯, in 68 quarts.

  • A π‘₯ 4 = 6 8 , π‘₯ = 2 7 2
  • B 6 8 π‘₯ = 4 , π‘₯ = 1 7
  • C 6 8 π‘₯ = 4 , π‘₯ = 1 1 7
  • D 4 π‘₯ = 6 8 , π‘₯ = 1 7
  • E π‘₯ + 4 = 6 8 , π‘₯ = 6 4

Q10:

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

Q11:

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

Q12:

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

Q13:

The equation 12𝑝=𝑐 shows the total cost 𝑐 of a trip to the movies in relation to the number of people 𝑝 that attend. If a trip cost $60, how many people attended?

Q14:

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

Q15:

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

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

Q16:

In the equation 𝑝=2𝑀, 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?

Q17:

The equation 𝑑=11π‘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=4𝑑 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:

The equation 𝑝=3𝑔 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?

Q20:

The equation 𝑠=2𝑏 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?

Q21:

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

Q22:

If 96π‘₯=96Γ—55, what is the value of π‘₯?

Q23:

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.

  • ATrue
  • BFalse

Q24:

The equation 5𝑔=35 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 Γ· 5
  • B 5 Γ· 3 5
  • C 3 5 Γ— 5
  • D 3 5 βˆ’ 5
  • E 3 5 + 5

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

What is the value of 𝑔?

Q25:

The equation 𝑔=2𝑛 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?

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