Grade by Grade
B. Number · Operations: Numbers to 100 000, Decimals, Fractions, Ratios and Rates

Estimating Sums and Differences of Decimals

B2.3 A1About 35 minutes
Learning goals
  • I can estimate sums and differences of decimal numbers up to hundredths.
  • I can round decimals to the nearest whole number, or use friendly numbers, to estimate.
  • I can use an estimate to decide if an answer is reasonable.
  • I can explain the strategy I used.

Words to know

estimate
A close guess that you can figure out quickly in your head.
round
Change a number to a nearby friendly number, like 3.89 → 4.
reasonable
An answer that makes sense because it is close to your estimate.
friendly numbers
Numbers that are easy to work with, like whole numbers, 0.25, 0.5 and 0.75.

Let's start at the store

Liam has a $12 bill. He wants to buy cereal for $3.89, apples for $2.15 and cheese for $4.98. Does he have enough money?

He doesn't need the exact total. He can estimate:

$3.89 is about $4. $2.15 is about $2. $4.98 is about $5.

4 + 2 + 5 = 11. About $11 is less than $12, so yes, he has enough.

(The exact total is $11.02, so his estimate was very close!)

Does Liam have enough with $12?cereal$3.89$4rounds to+apples$2.15$2rounds to+cheese$4.98$5rounds to4 + 2 + 5 = about $11. $11 < $12, so yes, he has enough!
Round each price to the nearest dollar, then add the easy numbers. The estimate (about $11) is close to the exact total of $11.02.

Strategy 1: Round to the nearest whole number

Look at the tenths digit.

  • If it is 5 or more, round up to the next whole number: 3.89 → 4, 6.5 → 7.
  • If it is less than 5, round down: 2.15 → 2, 7.42 → 7.

Then add or subtract the whole numbers in your head.

33.54
3.89 is between 3 and 4. It is much closer to 4, so 3.89 rounds to 4.
Worked example

Example 1: Estimate a difference

Estimate 9.04 − 2.97.

  1. 9.04 is about 9.
  2. 2.97 is about 3.
  3. 9 − 3 = 6.

9.04 − 2.97 is about 6. (Exact: 6.07)

Strategy 2: Use friendly numbers

Sometimes rounding to a whole number throws away too much. Use friendly decimals like 0.25, 0.5 and 0.75 instead.

0.48 + 0.26: rounding to whole numbers gives 0 + 0 = 0, which doesn't help. But 0.48 is about 0.5, and 0.26 is about 0.25. So the sum is about 0.75. (Exact: 0.74)

12.49 + 7.51: 12.49 is about 12.5 and 7.51 is about 7.5. 12.5 + 7.5 = 20. (Exact: 20.00)

Worked example

Example 2: Is the answer reasonable?

Jo used a calculator and got 3.45 + 2.6 = 60.5. Is that reasonable?

  1. Estimate: 3.45 is about 3, and 2.6 is about 3.
  2. 3 + 3 = 6.
  3. 60.5 is nowhere near 6, so Jo's answer is not reasonable. She probably pressed a wrong key.
  4. The exact answer is 3.45 + 2.6 = 6.05, which is close to 6. ✓

Not reasonable. The answer should be about 6.

Worked example

Example 3: Estimate, then decide

A jacket costs $47.85 on sale. It used to cost $62.10. About how much do you save?

  1. Round to whole dollars: $47.85 is about $48, and $62.10 is about $62.
  2. 62 − 48 = 14.

You save about $14. (Exact: $14.25)

Estimating tips

  • Estimate before you calculate, so you know about where the answer should be.
  • When you add: if both numbers were rounded up, the real sum is a bit less than your estimate. If both were rounded down, it is a bit more.
  • If the estimate is very close to the limit (like $10 when you have $10), work out the exact answer to be sure.
  • Tell someone how you estimated. There is often more than one good strategy.
Just for fun

Riddle: Why did the student bring a ladder to math class?

To help her round up!

Hands-on activity

Estimate the receipt

You need: a grocery receipt or flyer, paper and a pencil, and a calculator for checking.

  1. Choose 3 to 5 prices. Estimate the total by rounding each one to the nearest dollar. Write your estimate.
  2. Your grown-up chooses an amount of money, like $15 or $20. Decide: is there enough? How do you know?
  3. Use the calculator to find the exact total. How close was your estimate? Was it over or under? Why?
  4. Try again with friendly numbers like $0.25, $0.50 and $0.75. Was it closer?

Math talk: "When is an estimate good enough, and when do we need the exact answer?"

Your turn

1

Estimate 4.8 + 2.1.

2

Estimate 6.75 + 3.2.

3

Estimate 9.04 − 2.97.

4

Estimate 12.49 + 7.51 using friendly numbers.

5

Estimate 15.6 − 8.45.

6

Is 3.45 + 2.6 = 60.5 reasonable?

7

Is $10 enough for items costing $7.95 and $1.99?

More practice: warm-up

1

Round 4.7 to the nearest whole number.

2

Round 2.3 to the nearest whole number.

3

Estimate 3.9 + 1.1.

4

Estimate 7.2 − 2.8.

5

Round 6.49 to the nearest whole number.

More practice: on your own

1

Estimate 23.85 + 14.2.

2

Estimate 50.3 − 19.75.

3

Estimate 0.48 + 0.26 with friendly numbers.

4

It snowed 12.6 cm on Monday and 9.35 cm on Tuesday. About how much snow fell in all?

5

Mia says 4.37 − 1.9 = 3.47. Use an estimate to check. Is she right?

Challenge

1

Estimate 2.49 + 3.49 + 4.49 by rounding to whole numbers. Then estimate again using halves (2.5, 3.5, 4.5). Which estimate is closer? Why?

2

You have $10. Can you buy items costing $4.25, $3.80 and $1.95? Estimate first, then decide if you need the exact total.

3

From 3.6, 5.25, 4.4, 2.75, find two pairs that each add to exactly 8.

Check your understanding

Quiz

1.

What is the best estimate for 6.9 + 3.2?

2.

What is the best estimate for 9.85 − 4.1?

3.

Round 7.51 to the nearest whole number.

4.

Jo says 2.8 + 4.3 = 71. Is that reasonable?

5.

Use friendly numbers to estimate 0.26 + 0.74.

6.

About how much do 3 items at $2.99 cost?

For parents and teachers

Big idea: The Grade 5 curriculum (B2.3) asks students to estimate sums and differences of decimal numbers up to hundredths, and to explain their strategies. Estimating helps your child spot mistakes and make quick real-life decisions.

Common difficulties:

  • Rounding by the hundredths digit instead of the tenths digit (rounding 6.49 up to 7). For the nearest whole number, look only at the tenths.
  • Computing exactly, then rounding the answer. An estimate should be quick and done in the head.
  • Not using the estimate. Always compare the final answer to the estimate and ask "Does this make sense?"

How to help: At the grocery store, ask your child to keep a running estimate of the total. Before paying, ask "Will $20 be enough?" This lesson also supports A1 process skills: reasoning, reflecting on whether an answer makes sense, and communicating a strategy.