Questions: Measurement Conversions (Multi-Step)

Question 1

You have 2 feet 9 inches of rope and cut off 1 foot 11 inches. Which approach correctly solves this problem?

• A. Subtract column by column: feet minus feet (2 − 1 = 1) and inches minus inches (9 − 11 = −2 inches), giving 1 foot −2 inches
• B. Convert everything to inches first (33 − 23 = 10 inches = 0 feet 10 inches), then interpret the result
• C. Convert only the larger measurement to inches, leave the smaller in feet
• D. Ignore the unit mismatch and subtract the raw numbers: 29 − 111 = −82

Answer: (B)

When units are mixed within a quantity (feet and inches together), you must convert to a single unit before computing. Column-by-column subtraction fails here because 9 inches − 11 inches requires borrowing from the feet column — a step many students skip, producing a nonsensical negative. Converting to all inches first (2 ft 9 in = 33 in; 1 ft 11 in = 23 in) makes the subtraction straightforward: 33 − 23 = 10 inches.

Question 2

A recipe calls for 3 cups of milk per batch. You are making 5 batches. How many quarts of milk do you need? (4 cups = 1 quart)

• A. 5 quarts (1 quart per batch × 5 batches)
• B. 3.75 quarts (3 × 5 = 15 cups, then 15 ÷ 4 = 3.75 quarts)
• C. 20 quarts (3 × 5 = 15, then 15 × 4 = 60 — wait, ÷ 4, but some students multiply)
• D. 0.6 quarts (3 ÷ 5)

Answer: (B)

Step 1: multiply to get total cups (3 × 5 = 15 cups). Step 2: convert to quarts (15 ÷ 4 = 3.75 quarts). Here, computing comes first, then converting — because both measurements are in the same unit (cups) for the multiplication step. Option A confuses 'per batch' with 'per quart.' Option C is the classic error of multiplying instead of dividing by the conversion factor.

Question 3

In a multi-step measurement problem, the best strategy is typically to convert most units at the very end, after performing most calculations.

• T. True
• F. False

Answer: False

The timing of conversion depends on the problem structure. When units are mixed within a single quantity (e.g., 3 feet 7 inches), you must convert before computing, or the arithmetic breaks down. When all values share a common unit and you just need a different unit for the final answer, converting after computing works fine. 'Always convert at the end' is a false rule that fails on mixed-unit problems.

Question 4

Writing units as fractions and canceling them — for example, '6 cups × (1 quart / 4 cups) = 1.5 quarts' — is a reliable check that a conversion was set up correctly.

• T. True
• F. False

Answer: True

Unit cancellation is a built-in error-checker. If you set up the conversion factor correctly, the unwanted unit appears in both numerator and denominator and cancels, leaving only the target unit. If units do not cancel cleanly, the conversion factor is inverted or wrong. This technique works for any unit system and any number of conversion steps.

Question 5

Explain the 'convert before computing' vs. 'convert after computing' decision. When should you use each strategy?

Model answer: Convert before computing when units are mixed within the same quantity (e.g., 3 feet 7 inches), because you cannot operate on mixed units directly without errors. Convert after computing when all quantities already share a compatible unit and you only need the final answer in a different unit (e.g., multiply cups and then convert the total to quarts). The key question is: 'Are my units compatible for the operation I am about to do?'

A reliable habit: before any operation, check that all quantities involved have the same unit. If not, convert first. After the operation, check whether the answer unit matches what the problem asks for — if not, convert at the end. Keeping units written at every step makes both checks automatic.