L3 · Comparing and ordering fractions, including improper and mixed

Learning goal

“I can compare and order fractions - including improper fractions and mixed numbers - by testing them against the benchmarks 0, 1/2, and 1, and by counting parts when the denominator is the same.”

Benchmark — a known number used as a measuring post for comparison: 0, 1/2, and 1 are the benchmarks in this lesson.

Compare — decide whether one number is greater than (>), less than (<), or equal to (=) another.

Greater than (>) — the first number is larger: 7/8 > 1/2.

Less than (<) — the first number is smaller: 3/10 < 1/2.

Worked example

Compare 5/12 with 1/2. Step 1: Half of the whole means half of the parts. The whole has 12 parts, so half the whole is 6 parts: 6/12 = 1/2. Step 2: 5/12 counts only 5 parts - fewer than 6. So 5/12 < 1/2. Step 3: The equal case matters too: with denominator 8, half the whole is 4 parts, so 4/8 = 1/2 exactly. The test, said plainly: compare the numerator with HALF the denominator. Less than half -> less than 1/2. Equal to half -> equal to 1/2. More than half -> greater than 1/2. Model both ways: a bar in twelfths with the halfway line drawn at 6/12 and 5/12 shaded, AND a 0-2 number line in twelfths with 1/2 marked as the benchmark post and 5/12 just before it.

Check yourself — explain it

To test 7/10 against 1/2, what do you compare?

Paired problem — example still visible

Compare 3/8 with 1/2 -> half of 8 is 4; 3 < 4, so 3/8 < 1/2

Faded completion — last step is yours

"5/6 against 1/2: half of 6 is 3; 5 ___ 3, so 5/6 ___ 1/2." -> > ; >

Ready to practise?

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

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