Grade 10 — Mathematics 10-3 › T3U03 Linear Measurement Problems

Grade 10 › T3U03 Linear Measurement Problems › L4
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-M3/A1

L4 · Measurement arithmetic clinic: decimals and fractions

Learning goal

“I can add, subtract, multiply and divide decimal and fractional measurements accurately, build a real situation where a fractional measurement is divided by a fraction (3.7), judge whether a measurement answer is reasonable (3.9), and isolate an unknown in the perimeter/circumference formulas (A1).”

Mixed number — a whole number with a fraction: 3 5/8 in. Tape measures speak in mixed numbers; so do cut lists.
Common denominator — the shared fraction size that lets two fractions be added or subtracted: eighths with eighths, never eighths with quarters directly.
Reasonableness check — estimating the answer BEFORE or AFTER computing (rounding each measurement to a nearby whole number) and comparing. A measurement answer that fails this check is wrong, however neat the arithmetic looks.
Worked example

Two boards are joined end to end: 3 5/8 in and 2 3/4 in. Total length? Step 1 (common denominator): quarters must become eighths: 2 3/4 = 2 6/8. Step 2: Add wholes and parts: 3 + 2 = 5; 5/8 + 6/8 = 11/8. Step 3: 11/8 is more than a whole: 11/8 = 1 3/8, so the total is 5 + 1 3/8 = 6 3/8 in. Verify by estimating: about 3.6 + 2.75 ≈ 6.4, close.

Check yourself — explain it

Why rewrite 3/4 as 6/8 before adding?

Paired problem — example still visible

4 1/2 in + 1 3/8 in -> 5 7/8 in (4 4/8 + 1 3/8 = 5 7/8)

Faded completion — last step is yours

"Trim: 5 1/4 in - 2 5/8 in. Rename: 5 2/8 - 2 5/8. The top fraction is smaller - regroup 1 whole: 4 10/8 - 2 5/8 = ___ in." -> 2 5/8 in

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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