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🧩 6th grade math · Patterns & Algebra

Change units with ratios

1 foot = 12 inches is a ratio. Going to a smaller unit gives more of them: multiply. Going to a bigger unit gives fewer: 36 inches ÷ 12 = 3 feet.

Worked example

1 quart = 2 pints. How many pints are in 7 quarts?
quartspints00127?
Answer: 14 pints
Each quart is 2 pints. 7 × 2 = 14 pints.

For grown-ups: Unit conversion by ratio reasoning. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 6.RP.A.3d
What this practises, for teachers

Practices unit conversion by ratio reasoning (6.RP.A.3d). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

Try three

  1. 1 centimeter = 10 millimeters. How many millimeters are in 4 centimeters?
    centimetersmillimeters001104?
    Show the answer and how
    Answer: 40 millimeters
    Each centimeter is 10 millimeters. 4 × 10 = 40 millimeters.
  2. 1 gallon = 4 quarts. How many quarts are in 8 gallons?
    gallonsquarts00148?
    Show the answer and how
    Answer: 32 quarts
    Each gallon is 4 quarts. 8 × 4 = 32 quarts.
  3. 1 hour = 60 minutes. How many minutes are in 6 hours?
    hoursminutes001606?
    Show the answer and how
    Answer: 360 minutes
    Each hour is 60 minutes. 6 × 60 = 360 minutes.

Before and after

Learn first: Ratio tables and tapes (6th)

Comes next: Proportional or not? (7th)

Name: ____________________Date: ____________Score: ____ / 12

Change units with ratios (6th grade)

  1. 1 centimeter = 10 millimeters. How many millimeters are in 7 centimeters?
    centimetersmillimeters001107?
  2. 1 pint = 2 cups. How many cups are in 2 pints?
    pintscups00122?
  3. 1 meter = 100 centimeters. How many centimeters are in 8 meters?
    meterscentimeters0011008?
  4. 1 day = 24 hours. How many hours are in 9 days?
    dayshours001249?
  5. 1 gallon = 4 quarts. How many quarts are in 6 gallons?
    gallonsquarts00146?
  6. 1 foot = 12 inches. How many inches are in 4 feet?
    feetinches001124?
  7. 1 kilogram = 1000 grams. How many kilograms are in 4000 grams?
    kilogramsgrams0011000?4000
  8. 1 centimeter = 10 millimeters. How many millimeters are in 3 centimeters?
    centimetersmillimeters001103?
  9. 1 kilogram = 1000 grams. How many grams are in 7 kilograms?
    kilogramsgrams00110007?
  10. 1 year = 12 months. How many years are in 48 months?
    yearsmonths00112?48
  11. 1 pound = 16 ounces. How many pounds are in 32 ounces?
    poundsounces00116?32
  12. 1 quart = 2 pints. How many quarts are in 8 pints?
    quartspints0012?8

Answer key

  1. 70 millimeters
  2. 4 cups
  3. 800 centimeters
  4. 216 hours
  5. 24 quarts
  6. 48 inches
  7. 4 kilograms
  8. 30 millimeters
  9. 7000 grams
  10. 4 years
  11. 2 pounds
  12. 4 quarts

More 6th grade skills: all 6th grade math skills, or every grade at math skills.