L5 · Estimating products and quotients

Learning goal

“I can estimate a product or quotient by rounding to friendly numbers, and use the estimate to judge whether a calculated answer is reasonable.”

Estimate — a careful guess at an answer, made by rounding the numbers first. An estimate is close, not exact.

Round — replace a number with a nearby friendly number: 487 rounds to 500, 32 rounds to 30.

Compatible numbers — numbers that are easy to divide mentally because they fit together: for / 8, 720 is compatible because 72 / 8 = 9.

Reasonable — an answer is reasonable if it lands near the estimate. An answer ten times too big is not reasonable, even if the arithmetic "worked."

Worked example

Estimate 487 x 32. Step 1: Round each factor to a friendly number: 487 -> 500; 32 -> 30. Step 2: Multiply the friendly numbers: 500 x 30 = 15,000. Step 3: That is the estimate. The exact product (15,584, if you compute it) lands close to 15,000 - the estimate did its job: it tells you the answer's size before you compute. Say it plainly: an estimate is a fence, not a target. An answer of 1,558 or 155,840 for 487 x 32 would crash through the fence and expose a place-value slip immediately.

Check yourself — explain it

Why round BOTH factors instead of just one?

Paired problem — example still visible

Estimate 213 x 47. -> 200 x 50 = 10,000 (exact: 10,011).

Faded completion — last step is yours

"Estimate 618 x 52: round to ___ x ___ = ___" -> 600 x 50 = 30,000 (exact: 32,136)

Ready to practise?

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

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