L1 · Adding fractions: like and unlike denominators

Learning goal

“I can add any two positive fractions - like or unlike denominators - by rewriting them with the least common denominator, and I can explain why the denominators are never added.”

Least common denominator (LCD) — the smallest number that both denominators divide into evenly; the common denominator we choose first in Grade 7.

Equivalent fraction — a different name for the same amount (5/6 = 10/12); the value does not change when numerator and denominator are multiplied by the same number.

Sum — the result of an addition.

Simplify — rewrite a fraction in lowest terms by dividing numerator and denominator by the same number.

Worked example

Add 5/12 + 3/4. Step 1: The parts are different sizes - twelfths and quarters cannot be counted together yet. Step 2: 12 is a multiple of 4, so the denominators are related. Rewrite 3/4 in twelfths: 3/4 = 9/12. The amount did not change - only the size of the parts. Step 3: Now both fractions name twelfths. Add the numerators, keep the denominator: 5/12 + 9/12 = 14/12. Simplify: 14/12 = 7/6 = 1 1/6. The sum is bigger than 1 - that is fine. Both models agree: a bar split in twelfths with 5 twelfths + 9 twelfths shaded, and a 0-2 number line marked in twelfths - jump 5/12 from 0, then jump 9/12 more, land on 14/12 = 1 1/6. Say it plainly: the denominator names the size of the parts. We never add denominators, because we are counting parts, not changing their size.

Check yourself — explain it

Why do we change 3/4 into 9/12 before adding?

Paired problem — example still visible

3/10 + 2/5 -> 2/5 = 4/10, so 3/10 + 4/10 = 7/10

Faded completion — last step is yours

"7/9 + 1/3: 1/3 = 3/9, so 7/9 + 3/9 = ___" -> 10/9 = 1 1/9

Ready to practise?

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

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