Mathematics
Grade 4
15 min
Estimate products - multiply by larger numbers
Estimate products - multiply by larger numbers
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Introduction & Learning Objectives
Learning Objectives
Round multi-digit numbers to their greatest place value.
Estimate the product of a one-digit number and a multi-digit number.
Estimate the product of two multi-digit numbers.
Use estimation vocabulary like 'about', 'approximately', and the symbol '≈'.
Determine if an exact answer is reasonable by comparing it to an estimate.
A new video game costs $48. If you and 8 friends all want to buy it, about how much money would that be? 💰 Let's find a quick way to guess!
In this lesson, you will learn how to make smart guesses, called estimates, when you multiply large numbers. Estimating is a super-fast way to find an answer that is close to the exact one, which helps you check your work and solve problems in your head.
Real-Wo...
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Key Concepts & Vocabulary
TermDefinitionExample
EstimateAn answer that is close to the exact answer. We use the word 'about' when we estimate.An estimate for 29 + 52 is 80, because 30 + 50 = 80.
ProductThe answer you get when you multiply two or more numbers together.In 6 x 4 = 24, the number 24 is the product.
RoundingChanging a number to a simpler one that is close to the original number. We usually round to the nearest ten, hundred, or thousand.The number 38 can be rounded up to 40. The number 121 can be rounded down to 100.
FactorA number that is multiplied by another number to find a product.In 8 x 5 = 40, the numbers 8 and 5 are the factors.
Greatest Place ValueThe position of the digit that has the largest value in a number.In the number 4,825, the greatest place value is the thousands place (wher...
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Core Formulas
Rounding to Estimate Products
a \times b \approx \text{round}(a) \times \text{round}(b)
To estimate a product, round each factor to its greatest place value. Then, multiply the rounded numbers. The symbol '≈' means 'is approximately equal to'.
Multiplying with Zeros
(a \times 10) \times (b \times 10) = (a \times b) \times 100
When you multiply numbers that end in zeros, multiply the non-zero digits first. Then, count the total number of zeros in the factors and add them to the end of your product.
4 more steps in this tutorial
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Challenging
You estimate the product of 148 x 22 by calculating 100 x 20 = 2,000. Is the exact answer likely to be greater or less than 2,000, and why?
A.Greater, because 148 is a large number.
B.Greater, because both 148 and 22 were rounded down, so the estimate is an underestimate.
C.Less, because rounding always makes the answer smaller.
D.It is impossible to tell without finding the exact answer.
Challenging
The estimated product of two 2-digit numbers is 2,400. Which of the following could have been the original numbers?
A.28 and 51
B.38 and 62
C.59 and 24
D.78 and 43
Challenging
When we estimate 28 x 63, we round to 30 x 60 = 1,800. The exact answer is 1,764. Why is our estimate (1,800) slightly higher than the exact answer?
A.Because we rounded both factors down.
B.Because we forgot to add the zeros.
C.Because we should have rounded to the hundreds place.
D.Because we rounded one number up and one number down.
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