Grade by Grade
B. Number · Operations: Divisibility, Decimals, Fractions, Ratios and Percents

Adding and Subtracting Whole Numbers and Decimals

B2.4 B2.1About 45 minutes
Learning goals
  • I can estimate sums and differences before I calculate.
  • I can add and subtract whole numbers up to one million with the column algorithm.
  • I can add and subtract decimals to thousandths by lining up the decimal points.
  • I can check my answer with the inverse operation and my estimate.

Words to know

estimate
A close answer you find quickly, often by rounding, to know about how big the answer should be.
algorithm
A set of steps that always works, like adding in columns from right to left.
regroup
Trade 10 of one place value for 1 of the next place value, or the other way around.
thousandths
The third place to the right of the decimal point. 0.001 is one thousandth.
placeholder zero
A zero you write to fill an empty place, like writing 7.5 as 7.500. It doesn't change the value.

Remember from Grade 5

In Grade 5 you added and subtracted whole numbers up to 100 000 and decimals to hundredths. In Grade 6 the numbers grow: whole numbers up to one million and decimals to thousandths. The good news: the steps are exactly the same!

Let's start at the track meet

At a school track meet, Zoe throws the shot put 5.875 m on her first try and 6.2 m on her second try. How much farther was her second throw?

First estimate: about 6 − 6 = 0? That's too rough. Use tenths: 6.2 − 5.9 = 0.3. So the answer should be about 0.3 m.

Then calculate: 6.200 − 5.875 = 0.325 m. That is close to the estimate, so it makes sense.

Count up from 5.875 to 6.25.85.96.06.16.26.35.875+0.125+0.20.125 + 0.2= 0.325
Another way to find 6.2 − 5.875: hop up to the friendly number 6, then on to 6.2. The hops add to 0.325 m.

The steps

  1. Estimate first. Round to friendly numbers.
  2. Line up the place values. For decimals, line up the decimal points.
  3. Fill empty places with placeholder zeros (6.2 = 6.200).
  4. Add or subtract from right to left, regrouping when you need to.
  5. Check: Is the answer close to the estimate? For subtraction, add your answer to the number you took away.
Ones.TenthsHundredthsThousandths
6.200
−5.875
=0.325
Line up the decimal points. Write 6.2 as 6.200 so every place has a digit.
Worked example

Example 1: Add big whole numbers

348 275 + 196 849 = ?

  1. Estimate: 350 000 + 200 000 = 550 000.
  2. Ones: 5 + 9 = 14. Write 4, regroup 1 ten.
  3. Tens: 1 + 7 + 4 = 12. Write 2, regroup 1 hundred.
  4. Hundreds: 1 + 2 + 8 = 11. Write 1, regroup 1 thousand.
  5. Thousands: 1 + 8 + 6 = 15. Write 5, regroup 1 ten thousand.
  6. Ten thousands: 1 + 4 + 9 = 14. Write 4, regroup 1 hundred thousand.
  7. Hundred thousands: 1 + 3 + 1 = 5.
  8. 545 124 is close to 550 000. ✓

348 275 + 196 849 = 545 124

Worked example

Example 2: Subtract across zeros

600 000 − 237 458 = ?

  1. Estimate: 600 000 − 240 000 = 360 000.
  2. Trick: take 1 from both numbers. The difference stays the same, and there's no regrouping: 599 999 − 237 457.
  3. Subtract each column: 599 999 − 237 457 = 362 542.
  4. Check: 362 542 + 237 458 = 600 000. ✓

600 000 − 237 458 = 362 542

Take 1 from both numbers: the gap stays the same237 458600 000gap: 362 542237 457599 999gap: 362 542Both points moved 1 to the left (shift drawn bigger so you can see it).
Subtracting finds the distance between two numbers. Slide both numbers down by 1 and the distance does not change, but 599 999 − 237 457 needs no regrouping. Not to scale.
Worked example

Example 3: Add three decimals

12.6 + 3.475 + 0.89 = ?

  1. Estimate: 13 + 3 + 1 = 17.
  2. Line up the decimal points and add zeros: 12.600 + 3.475 + 0.890.
  3. Thousandths: 0 + 5 + 0 = 5. Hundredths: 0 + 7 + 9 = 16, write 6, regroup. Tenths: 1 + 6 + 4 + 8 = 19, write 9, regroup. Ones: 1 + 2 + 3 + 0 = 6. Tens: 1.
  4. 16.965 is close to 17. ✓

12.6 + 3.475 + 0.89 = 16.965

Worked example

Example 4: Subtract a decimal from a whole number

20 − 7.384 = ?

  1. Estimate: 20 − 7 = 13, a little less.
  2. Write 20 as 20.000.
  3. Count up: 7.384 + 0.616 = 8, and 8 + 12 = 20. So the difference is 12 + 0.616 = 12.616.
  4. Check: 12.616 + 7.384 = 20.000. ✓

20 − 7.384 = 12.616

Line up the points

The most common mistake with decimals is lining up the last digits instead of the decimal points. A whole number has a hidden decimal point at its end: 20 = 20.0 = 20.000.

Just for fun

Why did the decimal points line up so neatly?

The teacher said, "No cutting in line, or your answers will be wrong!"

Hands-on activity

Kitchen scale math

You need: a kitchen scale that shows grams, 3 or 4 food items (like an apple, a can and a box of pasta), paper and a pencil.

  1. Weigh each item. Write the mass in kilograms with three decimal places. (1000 g = 1 kg, so 182 g = 0.182 kg and 1 050 g = 1.050 kg.)
  2. Estimate the total mass. Then add to find it exactly.
  3. Find the difference between the heaviest and the lightest item.
  4. Put all the items on the scale together. Is the total close to your answer?

Math talk: "Why did you write 182 g as 0.182 kg and not 1.82 kg?"

Your turn

1

45 380 + 27 965 = ?

2

503 200 − 146 875 = ?

3

4.56 + 2.375 = ?

4

9.2 − 3.468 = ?

5

Estimate 18.94 + 6.207. Then find the exact answer.

6

1.25 + 0.6 + 3.405 = ?

7

Ana runs 100 m in 15.48 s. Ben runs it in 16.2 s. How much faster is Ana?

More practice: warm-up

1

0.3 + 0.4 = ?

2

1.5 + 2.5 = ?

3

10 − 0.5 = ?

4

7 000 + 3 000 = ?

5

0.25 + 0.005 = ?

More practice: on your own

1

287 609 + 412 395 = ?

2

1 000 000 − 375 820 = ?

3

15.07 − 8.759 = ?

4

You have $50. You buy boots for $27.86 and mittens for $12.49. How much is left?

5

Sam wrote 3.4 + 1.25 = 1.59. What went wrong? What is the right answer?

Challenge

1

Kai's long jump is 2.875 m. Lena's is 3.06 m. Who jumped farther, and by how much?

2

Three towns have populations of 24 865, 108 340 and 9 507. What is the total?

3

Find the missing number: 7.5 − ? = 2.836.

Check your understanding

Quiz

1.

What is 3.6 + 2.45?

2.

What is 8 − 2.375?

3.

Which is the best estimate for 24.89 + 5.103?

4.

What is 250 000 − 98 500?

5.

When you add decimals, what should you line up?

6.

What is 0.457 + 0.6?

For parents and teachers

Big idea: B2.4 asks Grade 6 students to represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms. In Grade 6 whole numbers go up to one million (B1.1) and decimals to thousandths (B1.4), so we practise with those sizes.

Common difficulties:

  • Lining up last digits instead of decimal points.
  • Regrouping across zeros (like 600 000 − 237 458). The "take 1 from both" trick helps.
  • Skipping the estimate. An estimate catches answers that are 10 times too big or too small.

How to help: Use real decimals: race times, receipts, and masses in kilograms from a kitchen scale. Ask "About how much will it be?" before every calculation.