L3 · Comparing and ordering fractions

Learning goal

“I can compare and order fractions using the same denominator, the same numerator, the benchmark 1/2, or renaming one fraction so the parts match.”

Compare — to decide which of two numbers is bigger, smaller, or if they are equal.

Benchmark — a known fraction you measure others against; our main benchmark is 1/2.

Order — to list numbers from smallest to biggest (or biggest to smallest).

Worked example

Worked example 1: Which is bigger, 3/8 or 5/8? Step 1: The denominators are the same - both name eighths, the same size of part. Step 2: Count the parts: 5 parts is more than 3 parts. 5/8 is bigger. Worked example 2: Which is bigger, 2/3 or 2/5? Step 1: The numerators are the same - both count 2 parts. Step 2: But the parts are different sizes. Thirds are bigger parts than fifths (a whole cut into 3 gives bigger pieces than a whole cut into 5). Step 3: 2 big parts beat 2 small parts. 2/3 is bigger. Model both ways: bars with the same shading count but different part sizes, AND the 0-2 line: 2/3 sits to the right of 2/5 - bigger numbers sit further right. Say the rule plainly: same numerator -> the fraction with the SMALLER denominator is bigger, because its parts are bigger.

Check yourself — explain it

Why is 2/5 smaller than 2/3, even though 5 is bigger than 3?

Paired problem — example still visible

Which is bigger, 4/9 or 7/9? -> 7/9 (same size parts, more of them)

Faded completion — last step is yours

"Compare 3/4 and 3/8: same numerator, so compare the parts - quarters are ___ than eighths, so 3/4 is ___." -> bigger; bigger

Ready to practise?

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

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