L2 · Subtracting fractions with common denominators

Learning goal

“I can subtract two fractions that share a denominator by decomposing - taking unit parts away while the part size stays the same - including subtracting from 1 whole and working with improper fractions, and I give the difference in simplest form.”

Decompose — break a quantity into unit parts: 7/8 decomposes into seven 1/8 parts, ready to work with.

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

Unit fraction — one equal part of a whole; subtraction removes unit parts, never changes their size. (Review from L1.)

Common denominator — the same denominator in both fractions, so both count the same size of part. (Review from L1.)

Worked example

7/8 - 3/8. Step 1: Decompose 7/8 into seven 1/8 parts. Both fractions count eighths - same part size. Step 2: Take away 3 of the eighth-parts. The parts that remain are still eighths; their size never changed. Step 3: 7 - 3 = 4 parts left: 4/8. Simplify: 4/8 = 1/2. Model both ways: a bar in eighths with 7 shaded and 3 crossed out, AND a 0-2 number line in eighths: start at 7/8, jump back 3 eighths, land on 4/8 = 1/2. Say it plainly: subtraction removes parts. It never touches the denominator, because the denominator is the size of the parts, not a count of them.

Check yourself — explain it

Why does the denominator stay 8 in 7/8 - 3/8?

Paired problem — example still visible

5/6 - 1/6 -> 4/6, simplified: 2/3

Faded completion — last step is yours

"9/11 - 4/11: count the elevenths left after taking 4 away from 9: ___ elevenths, written ___/11." -> 5; 5/11

Ready to practise?

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

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