Lesson Worksheet: One-step Equations: Multiplication and Division Mathematics • 6th Grade

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

Q1:

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

  • A12π‘₯=24
  • B10π‘₯=60
  • C3π‘₯=18
  • D4π‘₯=24

Q2:

It takes JamesΒ 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.

  • A5π‘₯=65, π‘₯=13
  • B75π‘₯=5, π‘₯=15
  • C70π‘₯=5, π‘₯=14
  • D5π‘₯=70, π‘₯=14
  • E65π‘₯=5, π‘₯=13

Q3:

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

Q4:

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?

Q5:

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.

Q6:

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

  • Aπ‘₯4=68, π‘₯=272
  • B68π‘₯=4, π‘₯=17
  • C68π‘₯=4, π‘₯=117
  • D4π‘₯=68, π‘₯=17
  • Eπ‘₯+4=68, π‘₯=64

Q7:

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

  • A𝑐=112β„Ž
  • B𝑐=15β„Ž
  • C𝑐=5+β„Ž
  • D𝑐=5β„Ž
  • E𝑐=12β„Ž

Q8:

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.

  • Aπ‘₯βˆ’8=40
  • Bπ‘₯=8Γ—40
  • C8Γ—π‘₯=40
  • D8+π‘₯=40

Q9:

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

Q10:

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?

Q11:

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.

Q12:

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

  • Aβˆ’1
  • Bβˆ’π‘’
  • Cβˆ’1𝑒
  • D𝑒
  • E1𝑒

Q13:

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?

Q14:

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

Q15:

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

Q16:

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

Q17:

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

Q18:

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?

Q19:

Use the diagram to solve the equation 𝑠11=132.

  • A𝑠=1,584
  • B𝑠=1,331
  • C𝑠=12
  • D𝑠=13
  • E𝑠=1,452

Q20:

The product of π‘₯ and 2 is 154. What is the value of π‘₯?

Q21:

The shown table represents customary system conversions for some capacity units. Write an equation that can be used to find the number of cups in 816 teaspoons, and then solve it.

Capacity Unit1 tablespoon1 cup
Equivalent3 teaspoons16 tablespoons
  • A816π‘₯=16, π‘₯=151
  • B163π‘₯=816, π‘₯=153
  • C16π‘₯=816, π‘₯=51
  • D3(16π‘₯)=816, π‘₯=17
  • E816π‘₯=3(16), π‘₯=117

Q22:

The given table demonstrates the customary system conversions for capacity units. By using this table, write and solve an equation to determine how many gallons there are in 176 pints.

Capacity Unit1 quart1 gallon
Equivalent Capacity Unit2 pints4 quarts
  • A8π‘₯=176, π‘₯=22
  • B176π‘₯=4, π‘₯=144
  • C4π‘₯=176, π‘₯=44
  • D2π‘₯=176, π‘₯=88
  • E176π‘₯=8, π‘₯=122

Q23:

Scarlett’s farm has 16 cows. Every month, her cows eat 2,880 bushels of grain. Assuming that there are 30 days in a month, write and solve an equation to determine the number of bushels of grain a single cow eats per month, and then find the number of bushels of grain a single cow eats per day.

  • A16π‘₯=2,880, 180 bushels per month, 6 bushels per day
  • Bπ‘₯βˆ’16=2,880, 2,896 bushels per month, 96 bushels per day
  • Cπ‘₯βˆ’16=2,880, 2,864 bushels per month, 95 bushels per day
  • Dπ‘₯+16=2,880, 2,864 bushels per month, 95 bushels per day
  • E16π‘₯=2,880, 210 bushels per month, 6 bushels per day

Q24:

The population of a small town is increasing at a rate of 335 people per year. Write and solve a multiplication equation to find how long it will take the population to increase by 4,020.

  • A4,020π‘₯=335, 12 years
  • B335π‘₯=4,020, 12 years
  • C335π‘₯=4,020, 112 years
  • D335π‘₯=4,020, 11 years
  • E4,020π‘₯=335, 112 years

Q25:

Given that π‘₯Γ—9=βˆ’18 find the value of π‘₯.

  • Aπ‘₯=βˆ’12
  • Bπ‘₯=12
  • Cπ‘₯=2
  • Dπ‘₯=βˆ’2

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