L1 · Adding fractions with common denominators

Learning goal

“I can add two fractions that share a denominator by composing unit fractions - the denominator stays the same because the size of the parts does not change - and I give the sum in simplest form, as a mixed number when it is greater than 1.”

Unit fraction — one equal part of a whole, like 1/8. Every fraction is a count of unit fractions.

Compose — put unit parts together to build a quantity: 3/8 is composed of three 1/8 parts.

Common denominator — the same denominator in both fractions, so both count the same size of part.

Sum — the result of an addition.

Worked example

3/8 + 2/8. Step 1: Both fractions count eighths - the same size of part. The unit fraction is 1/8. Step 2: 3/8 is composed of three 1/8 parts; 2/8 is two more. Put them together: 3 parts + 2 parts = 5 parts, and every part is still an eighth. Step 3: 3/8 + 2/8 = 5/8. The denominator stays 8 because adding parts does not change the size of the parts. The same idea builds a whole: eight 1/8 parts compose 8/8 = 1. Model both ways, side by side: a bar in eighths with 3 shaded, then 2 more shaded, AND a 0-2 number line marked in eighths: jump 3/8 from 0, then jump 2/8 more, land on 5/8. Say it plainly: adding fractions with a common denominator is counting - and counting never changes what you are counting.

Check yourself — explain it

Why does the denominator stay 8 in 3/8 + 2/8 = 5/8?

Paired problem — example still visible

1/6 + 4/6 -> count the sixths: 5/6

Faded completion — last step is yours

"2/9 + 5/9: both fractions name ninths, so add the counts: ___ ninths, written as ___/9." -> 7; 7/9

Ready to practise?

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

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