Lesson 7: Ratio Reasoning: Convert Measurements Between Systems6.AT.3c

I can…

I can use ratio reasoning to convert measurements between the customary and metric systems.

Key words

• Convert Measurements Between Systems — Rewriting a customary measurement as a metric one, or the reverse, so two amounts can be compared.
• Conversion factor — The ratio that links a unit in one system to a unit in the other, such as 1 mile to about 1.609 kilometers.
• Customary system — The measurement system used in the United States: inches, feet, miles, ounces, pounds, cups, quarts, gallons.
• Metric system — The measurement system used in most of the world, built on tens: centimeters, meters, kilometers, grams, kilograms, liters.
• Approximately — Close to, but not exactly equal. A rounded conversion factor gives an approximate result, written with ≈; an exact conversion uses =.
• Ratio table — A table of equal ratios used to scale a conversion factor up to the amount you actually need.
• Reasonableness — Checking that the size of an answer makes sense for the situation.
• Multi-step problem — A problem that needs two or more operations done in order.

Steps

1. Evelyn sees a Canadian highway sign reading 100 kilometers per hour and wonders whether that is faster or slower than 100 miles per hour.
2. Kilometers are metric and miles are customary, so 100 and 100 cannot be compared as they stand. Both measure distance, so a conversion factor links them: 1 kilometer ≈ 0.6 mile, or the ratio 1 : 0.6.
3. I build a ratio table from that unit ratio. Kilometers 1, 10, 100 pair with miles 0.6, 6, 60 — each column multiplies both numbers by the same factor.
4. So 100 kilometers ≈ 60 miles, which means 100 kilometers per hour ≈ 60 miles per hour.
5. Now the comparison is fair: 100 miles per hour is faster, because in one hour you would travel 100 miles instead of only about 60.

Try it

A bag of rice from a market in Mexico weighs 5 kilograms. Using 1 kg ≈ 2.2 lb, is the bag heavier or lighter than 5 pounds?

Check your answer

Heavier — 5 kg is about 11 lb

Scale the conversion factor: 2.2 × 5 = 11, so 5 kilograms ≈ 11 pounds — heavier than 5 pounds.

Sentence starter

I know ___ because ___.

Goal: I can explain a conversion between systems using the words conversion factor, approximately, customary, and metric.