L5 · Comparing fractions of the same whole: same denominator; same numerator

Learning goal

“I can compare two fractions of the SAME whole: with the same denominator, more parts is more; with the same numerator, the bigger denominator means smaller parts - and I can write the comparison with < or >.”

Same whole — comparisons in this lesson are only fair when both fractions come from wholes of the same size.

Greater than (>) — the symbol for "is more than": 6/7 > 4/7 reads "six sevenths is greater than four sevenths."

Less than (<) — the symbol for "is less than": 4/7 < 6/7. The symbol always points at the smaller amount.

Worked example

Two strips, THE SAME SIZE - the same whole. Both are split into 7 equal parts. Strip A has 4/7 shaded. Strip B has 6/7 shaded. The parts are the SAME SIZE in both strips (both are sevenths of the same whole). So the comparison is just a count: 6 parts is more than 4 parts. 6/7 > 4/7. Rule: same denominator, same whole - the bigger numerator is the bigger fraction. You are counting identical parts.

Check yourself — explain it

Why can we compare 4/7 and 6/7 just by counting parts?

Paired problem — example still visible

Same whole, split into ninths: compare 5/9 and 3/9. -> 5/9 > 3/9 (5 parts of the same size beats 3)

Faded completion — last step is yours

"Same whole, eighths: 2/8 ___ 7/8 (write < or >)." -> <

Ready to practise?

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

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