Estimate Products and Quotients
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What you will learn
- 1Estimate multiplication products by rounding factors to the nearest ten or hundred
- 2Estimate division quotients using compatible numbers
- 3Determine whether an estimate is an overestimate or underestimate
- 4Use estimation to check the reasonableness of exact answers
Mini Lesson
Estimating before you calculate helps you decide whether your answer makes sense. For multiplication, round one or both factors to a nearby ten or hundred. For division, choose a compatible number — one that divides evenly — close to the dividend.
Round to Estimate Products
- Round the factor to the nearest ten or hundred, then multiply.
- Example: 38 × 7 — round 38 up to 40 → 40 × 7 = 280 (estimate).
- Because you rounded UP, the estimate (280) is greater than the exact answer (266) — this is an overestimate.
Compatible Numbers for Division
- A compatible number is one that can be divided evenly by the divisor.
- Example: 193 ÷ 6 — 180 is close to 193 and 180 ÷ 6 = 30, so 30 is the estimate.
- Because 180 < 193, you rounded DOWN, making 30 an underestimate.
Over- and Underestimates
- Rounding UP a factor → overestimate (estimate > exact answer).
- Rounding DOWN a factor → underestimate (estimate < exact answer).
- Knowing which type of estimate you made helps you evaluate your exact answer.
Why Estimate?
- Check reasonableness: if your exact answer is far from the estimate, recheck your work.
- Real-life situations where an exact value is not needed (shopping totals, travel time).
- Mental math: estimates are faster to compute than exact answers.
Words to know
Product
The answer to a multiplication problem
e.g. The product of 23 and 4 is 92.
Quotient
The answer to a division problem
e.g. The quotient of 96 ÷ 12 is 8.
Compatible numbers
Friendly numbers that are easy to multiply or divide
e.g. 50 and 25 are compatible numbers for division.
Overestimate
An estimate that is greater than the exact answer
e.g. Rounding 47 up to 50 gives an overestimate.
Underestimate
An estimate that is less than the exact answer
e.g. Rounding 47 down to 40 gives an underestimate.
Tip: for division, ask "what multiple of the divisor is closest to the dividend?" That multiple is your compatible number.
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