Estimation in multiplication
This is a complete lesson with instruction and exercises about using estimation in multiplication, meant for 5th or 6th grade. To estimate, students round two and threedigit numbers before multiplying, but this rounding can be done in several different ways. Various exercises and word problems follow.
To estimate the result of multiplication (product), round the numbers to some close numbers that you can easily multiply mentally. One method of estimation is to round all
factors to the biggest digit (place value) they have. For example, estimate 365 × 24. Round 365 to the nearest hundred, and 24 to the nearest ten. So 365 ≈ 400, and 24 ≈ 20. Then 365 × 24 ≈ 400 × 20 = 8000. This way the multiplication is easy to do since it is only a matter of a single digit (4) times a single digit (2), and tagging zeros to the end (000). Look at other examples:

Practice
1. Estimate the products by rounding the factors to the biggest place value.
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 in
calculations. For example, if you estimate the result to be 5000, and you
calculate 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?

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.
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 can use various ways to estimate as you see fit. Or, try two different methods of 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 of
them.
Make an estimation of the cost.
Based on your estimation, will $10 be enough money for your purchase?