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Grade 9 · Math · Algebra 1

9th grade Convert rates and units in several steps worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Convert rates and units in several steps

Grade 9 Math Worksheet - Building Confidence

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Circle the best answer.

  1. A pool holds 200 liters and fills at 90 liters per hour. Ren writes L for the liters after m minutes. Which equation is right?

    • L = 200 + 90m
    • L = 200 + 5,400m
    • L = 1.5m
    • L = 200 + 1.5m

  2. A phone has 28 GB of data and uses 14 GB per week. Pia writes D for the GB left after d days. Which equation is right?

    • D = 28 - 14d
    • D = -2d
    • D = 28 - 98d
    • D = 28 - 2d

  3. A taxi charges $3 plus $1.80 per mile. Milo writes C for the cost of a ride of k kilometers (1 mile = 1.6 km). Which equation is right?

    • C = 1.125k
    • C = 3 + 2.88k
    • C = 3 + 1.8k
    • C = 3 + 1.125k

  4. A plant is 12 cm tall and grows 2.1 cm per day. Kira writes H for the height after w weeks. Which equation is right?

    • H = 12 + 2.1w
    • H = 14.7w
    • H = 12 + 0.3w
    • H = 12 + 14.7w

  5. Tala's car travels 30 miles per gallon, and gas costs $3.60 per gallon. Which expression gives the cost in dollars per mile?

    • 30 ÷ 3.60
    • 3.60 × 30
    • 3.60 ÷ 30
    • 3.60 + 30

  6. A hose delivers 1,500 liters per hour. Zee wants the liters per minute. Which expression gives it?

    • 60 ÷ 1,500
    • 1,500 ÷ 60
    • 1,500 × 60
    • 1,500 + 60

  7. A printer uses 2 cartridges per 1,500 pages, and each cartridge costs $18. Bo wants the dollars per page. Which expression gives it?

    • 2 × 18 × 1,500
    • (2 + 18) ÷ 1,500
    • 2 × 18 ÷ 1,500
    • 1,500 ÷ (2 × 18)

  8. The cost C in dollars of k kilowatt-hours is C = 0.08k + 5. Esme asks: what does 0.08 tell us?

    • Each extra dollar of cost uses 0.08 kilowatt-hours.
    • Each extra kilowatt-hour adds $0.08 to the cost.
    • The cost is $0.08 when no electricity is used.
    • The total cost for any amount of electricity is $0.08.

  9. A rider's distance D in km after t hours is D = 18t + 4. Noah asks: what does 18 tell us?

    • The rider covers 18 km in total.
    • The rider covers 18 km each hour.
    • Each kilometer takes the rider 18 hours.
    • The rider starts 18 km from the start line.

  10. A pool's volume V in liters after m minutes of draining is V = 900 - 45m. Ari asks: what does 45 tell us?

    • The pool loses 45 liters each minute.
    • The pool loses 45 liters in total.
    • The pool starts with 45 liters.
    • Each liter drained takes 45 minutes.
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9th grade Convert rates and units in several steps worksheet – printable
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About this worksheet

Convert rates and units in several steps. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can write an equation from a rate and a starting amount, changing the rate to the unit of my variable.
  • I can rewrite a linear model in a new unit and tell that the rate changes but the fixed fee does not.
  • I can compare two rates given as a table and as an equation, and tell when one plan becomes cheaper.
  • I can change square and cubic units, chain three rates, and judge a claim by converting both sides.

Standard: N-Q.A.1

Words to know

conversion fact: A pair that names the same amount two ways: 1 foot = 12 inches.

rate: A comparison of two different units, like $6 for each yard.

rate of change: How much the output changes for each one step of the input: the number beside the letter.

starting amount: The value when the input is 0: the number added or subtracted.

square unit: A unit for area: a square yard is a square 3 feet long and 3 feet wide.

break-even: The point where two plans cost the same.

Common mistakes

Your child used the number as given without changing its unit.

Your child multiplied where the conversion needs dividing, or the reverse.

Your child found the rate but left out the amount at the start.

What to say

Ask: does the rate say per hour while the variable counts minutes?

Ask: is the new unit bigger or smaller, so should the number get smaller or bigger?

Ask: what is the value when the time is zero?

Questions parents ask

What is the most common mistake with convert rates and units in several steps?

Your child used the number as given without changing its unit.

How can I help my child with convert rates and units in several steps?

Ask: does the rate say per hour while the variable counts minutes?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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