Estimation in multiplication (2024)

Practice

1. Estimate the products by rounding the factors to the biggest placevalue.

a. 158 × 32

≈ 200 × 30 = 6000

c. 29 × 94

≈ ____ × ___ = ____

d. 770 × 33

≈ ____ × ___ = ____

f. 88 × 99

≈ ____ × ___ = ____

j. 486 × 21

≈ ____ × ___ = ____

l. 209 × 27

≈ ____ × ___ = ____

2. One purpose of estimation is to catch gross errors incalculations. For example, if you estimate the result to be 5000, and youcalculate it to be 354, you know something is wrong since you're way off.
What is best estimate of the options given?

1. 103 × 52

2. 42 × 76

3. 319 × 25

4. 17 × 17

5. 99 × 59

6. 47 × 21

a. 6500

a. 4000

a. 6000

a. 1000

a. 6000

a. 470

b. 500

b. 320

b. 750

b. 200

b. 900

b. 9700

c. 5000

c. 4800

c. 9000

c. 400

c. 9000

c. 1000

3. Which product is the furthest from its estimate? Can you see why?

Estimations:

236 × 28 ≈

198 × 28 ≈

246 × 28 ≈

178 × 28 ≈

Exact products:

236 × 28 =

198 × 28 =

246 × 28 =

178 × 28 =

Other methods of estimation

When you round both factors to the biggest place value, 249 × 34 would be estimated to 6000; yet the actual product is 8466 - quite far from the estimate.

You get a much better estimate if you round 249 to 250, and not to 200. Round 34 still to 30. So 249 × 34 ≈ 250 × 30. To calculate this, first go 3 × 25 = 25 + 25 + 25 = 75, and then tag two zeros to it: 250 × 30 = 30 × 250 = 7500.
So instead of rounding to nearest hundred, you can round to the 'middle fifty' if the number is close to it.

Or, even when the number has hundreds, you can round to nearest ten. For example, 178 × 28 is better estimated to 180 × 30 - rounding both numbers to nearest ten. That you can do mentally by going 100 × 30 + 80 × 30, which is 3000 + 2400 = 5400.

You can also try to account for the error in your estimation by rounding one factor up, the other down - especially if you have to round one factor a lot. For example, 144 × 24. If you round 144 down to 100, round 24 up to 30 to make up for some of the error.

Estimation is not an exact science but a matter of rounding to close numbers that you can work in your head.

4. Estimate first, and then calculate the actual product.You canuse various ways to estimate as you see fit. Or, try two different methodsof estimation and compare which was more accurate.

	Estimations:	Reality:
a.	143 × 27 ≈ ________ × _________ = __________	143 × 27 = _________
b.	657 × 13 ≈ ________ × _________ = __________	657 × 13 = _________
c.	411 × 9 ≈ ________ × _________ = __________	411 × 9 = _________
i.	406 × 19 ≈ ________ × _________ = __________	406 × 19 = _________
k.	243 × 24 ≈ ________ × _________ = __________	243 × 24 = _________
l.	37 × 258 ≈ ________ × _________ = __________	37 × 258 = _________

5. Solve the word problems. If necessary, round the numbers to make an estimate.

a. Nelly counted the matches in a match box and got 58.
How many matches approximately are in 8 boxes?

Each day Nelly uses 10 matches.How long approximately will those 8 boxes last her?

b. Aunt Jeanie's chickens lay about 130 eggs a day.
Can she supply all the eggs for the above school within one week?
Note, her chickens lay eggs 7 days a week.

c. One (food) can costs 58 cents, and you're going to buy 18 ofthem.
Make an estimation of the cost.

Based on your estimation, will $10 be enough money for your purchase?

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Estimation in multiplication (2024)

Practice

References