L3 · Subtracting fractions: like and unlike denominators

Learning goal

“I can subtract any two positive fractions by rewriting them with a common denominator, jumping back on the number line - and I can check my answer is sensible with benchmarks.”

Difference — the result of a subtraction; how much is left, or how far apart two amounts are.

Benchmark — a familiar reference fraction - 0, 1/2, 1 - used to estimate and check whether an answer is a sensible size.

Common denominator — the same denominator for both fractions, so both name the same size of part (LCD from L1).

Simplest form — a fraction rewritten in lowest terms (6/9 in simplest form is 2/3).

Worked example

Subtract 7/8 - 1/4. Step 1: The parts are different sizes. You can only count back parts that match the parts you start with, so rewrite 1/4 in eighths: 1/4 = 2/8. Step 2: 7/8 - 2/8 = 5/8. Both models agree: an eighths bar with 7 parts shaded and 2 crossed out, and a 0-2 number line in eighths - start at 7/8, jump back 2/8, land on 5/8. Say it plainly: subtraction counts back parts of the same size. The denominator does not change, because the size of the parts does not change.

Check yourself — explain it

Why must 1/4 become 2/8 before subtracting?

Paired problem — example still visible

5/6 - 1/3 -> 1/3 = 2/6, so 5/6 - 2/6 = 3/6 = 1/2

Faded completion — last step is yours

"11/12 - 3/4: 3/4 = 9/12, so 11/12 - 9/12 = ___" -> 2/12 = 1/6

Ready to practise?

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

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