L5 · Estimating Products and Quotients

Learning goal

“I can estimate a product by rounding the 3-digit number to a friendly number, estimate a quotient using a compatible number, and use my estimate to judge whether a calculated answer is reasonable.”

Estimate — a smart, quick calculation with friendlier numbers that tells you about how big the answer should be. 312 x 4 is about 300 x 4 = 1,200.

Compatible number — a number close to the real one that divides (or multiplies) cleanly: for 642 / 8, use 640 because 640 / 8 = 80 exactly.

Reasonable — an answer is reasonable if it lands close to the estimate. 1,248 is reasonable for 312 x 4; 248 is not.

Worked example

Estimate 312 x 4. Step 1: Round the 3-digit number to the nearest hundred: 312 -> 300. Step 2: Multiply the friendly numbers: 300 x 4 = 1,200. So 312 x 4 is about 1,200. The exact product (L3 algorithm) is 1,248 - close to the estimate, so it is reasonable. An answer of 248 would fail the estimate instantly: it is not even in the right neighbourhood. The estimate is not the answer's replacement - it is the answer's BODYGUARD. It runs ahead and reports back what size of answer to expect.

Check yourself — explain it

We round 312 to 300 (not up to 400) because...

Paired problem — example still visible

Estimate, then compute: 287 x 3 -> estimate 300 x 3 = 900; exact: 861 - reasonable.

Faded completion — last step is yours

"Estimate 518 x 6: 518 -> 500; 500 x 6 = ___. So the exact answer should be near ___." -> 3,000; 3,000 (exact product: 3,108)

Ready to practise?

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

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