L5 · Fraction problem-solving clinic (results simplified)

Learning goal

“I can solve word problems with fractions and mixed numbers that share a denominator: I choose the operation from the story, estimate the answer against benchmarks first, compute with the strategy that fits, give the result in simplest form, and check it.”

Estimate — a quick benchmark-based guess made before computing (rounding each amount to 0, 1/2, or the next whole) so a wrong answer can be spotted.

Verify — prove an answer afterwards: add a difference back, or recompute with the other strategy.

Operation — the choice the story demands: joining amounts means add; removing or comparing amounts means subtract.

Worked example

Joining story: a jug holds 3/8 L of water. You pour in 2/8 L more. How much is in the jug? The amounts join -> add: 3/8 + 2/8 = 5/8 L. Removing story, same numbers: a jug holds 3/8 L of water. You pour out 2/8 L. How much is left? An amount is removed -> subtract: 3/8 - 2/8 = 1/8 L. Say it plainly: the numbers do not choose the operation - the story does. Estimate first: a tank holds 5 2/6 L. A hose adds 1 3/6 L. Estimate: 5 2/6 is near 5 1/2 - round to about 5 - and 1 3/6 is about 1 1/2, so the answer should be near 7, a little under. Exact: wholes 6, parts 5/6 -> 6 5/6 - inside the estimate's promise.

Check yourself — explain it

Two problems use 3/8 and 2/8 but need different operations. What decides?

Paired problem — example still visible

A ribbon is 7/8 m. A 3/8 m piece is joined to it. New length? -> removal is not happening; joining -> 7/8 + 3/8 = 10/8 = 1 1/4 m

Faded completion — last step is yours

"A tank is 9/10 full; 4/10 is drained. The story removes, so subtract: 9/10 - 4/10 = ___/10 = ___/2 in simplest form." -> 5/10; 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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