Grade by Grade
B. Number · Operations: Numbers to 10 000, Decimal Tenths, Multiplying and Dividing

Adding and Subtracting Decimal Tenths

B2.4About 40 minutes
Learning goals
  • I can line up decimal points to add and subtract.
  • I can regroup 10 tenths as 1 whole, and 1 whole as 10 tenths.
  • I can solve story problems with decimal tenths.

Words to know

decimal point
The dot between the ones and the tenths, like in 12.4.
tenths place
The first place to the right of the decimal point.
regroup
Trade 10 tenths for 1 whole, or 1 whole for 10 tenths.

Let's start with a story

It snowed 12.5 cm on Monday and 8.7 cm on Tuesday. How much snow fell in the two days?

These numbers are too tricky to add in your head quickly. Good news: the column method works for decimals too!

The golden rule: line up the decimal points

When you add or subtract decimals, line up the decimal points. Then tenths are under tenths, ones under ones and tens under tens.

Put the decimal point in your answer right below the other decimal points.

If a number is a whole number, like 9, write it as 9.0. It's the same number: 9 wholes and 0 tenths.

Regrouping with tenths

  • When the tenths add up to 10 or more, regroup 10 tenths as 1 whole. Carry 1 into the ones column.
  • When you subtract and don't have enough tenths, regroup 1 whole as 10 tenths.
Worked example

Example 1: Adding tenths

Solve 12.4 + 7.8.

  1. Estimate: 12 + 8 = 20.
  2. Line up the decimal points.
  3. Tenths: 4 + 8 = 12 tenths. Write 2, carry 1 whole.
  4. Ones: 1 + 2 + 7 = 10. Write 0, carry 1 ten.
  5. Tens: 1 + 1 = 2.
  6. Put the decimal point in the answer under the others.

12.4 + 7.8 = 20.2. Close to 20. ✓

tOT114.218.7+2.02
12.4 + 7.8 in columns. T = tens, O = ones, t = tenths. The decimal points line up, and the small 1s are regrouped.
Worked example

Example 2: The snow story

Solve 12.5 + 8.7.

  1. Estimate: 13 + 9 = 22.
  2. Tenths: 5 + 7 = 12 tenths. Write 2, carry 1.
  3. Ones: 1 + 2 + 8 = 11. Write 1, carry 1.
  4. Tens: 1 + 1 = 2.

21.2 cm of snow fell. Close to 22. ✓

Worked example

Example 3: Subtracting tenths

Solve 15.3 − 6.7.

  1. Estimate: 15 − 7 = 8.
  2. Tenths: 3 − 7? Not enough. Regroup 1 whole as 10 tenths: 13 − 7 = 6. (Ones: 5 becomes 4.)
  3. Ones: 4 − 6? Not enough. Regroup 1 ten as 10 ones: 14 − 6 = 8. (Tens: 1 becomes 0.)
  4. Tens: 0. Nothing to write.
  5. Check: 8.6 + 6.7 = 15.3. ✓

15.3 − 6.7 = 8.6

tOT131403.517.6−6.8
15.3 − 6.7 with regrouping. 1 whole became 10 tenths, and 1 ten became 10 ones.
Worked example

Example 4: Subtracting from a whole number

A ribbon is 9 m long. Ana cuts off 3.4 m. How much is left?

  1. Write 9 as 9.0 so it has a tenths place.
  2. Tenths: 0 − 4? Regroup 1 whole: 10 − 4 = 6. (Ones: 9 becomes 8.)
  3. Ones: 8 − 3 = 5.
  4. Check: 5.6 + 3.4 = 9.0. ✓

5.6 m is left.

Where's the point?

Before you start, say the estimate out loud. After you finish, look at your answer: is the decimal point in the right place? If you got 2.02 when you expected about 20, the decimal point is lost!

Just for fun

Always line up the decimal points. Crooked decimal points are like crooked skate blades: you'll end up somewhere you didn't plan to go!

Hands-on activity

Hallway long jump

You need: a measuring tape or metre stick, masking tape, paper and a pencil. Jump on a clear floor or outside on grass, and wear shoes that don't slip.

  1. Put a tape line on the floor. Stand behind it and do a standing long jump.
  2. A grown-up measures from the line to your back heel. Round to the nearest tenth of a metre (10 cm). For example, 120 cm is 1.2 m, and 98 cm rounds to 1.0 m.
  3. Jump 3 times and record each jump in metres.
  4. Add your first two jumps with the column method.
  5. Subtract to find the difference between your longest and shortest jump.
  6. Have your grown-up jump too. Who jumped farther? By how much?

Your turn

1

3.4 + 2.5 = ?

2

6.8 + 1.7 = ?

3

14.6 + 9.5 = ?

4

8.7 − 3.2 = ?

5

12.3 − 4.8 = ?

6

10 − 2.6 = ?

7

A pumpkin has a mass of 6.4 kg and a squash has a mass of 2.9 kg. What is their total mass?

More practice: warm-up

1

1.2 + 1.3 = ?

2

4.5 + 2.0 = ?

3

5.9 − 1.4 = ?

4

7.5 − 0.5 = ?

5

2.2 + 3.3 = ?

More practice: on your own

1

23.6 + 18.7 = ?

2

30 − 12.4 = ?

3

45.2 − 27.9 = ?

4

Two ski trails are 3.5 km and 2.8 km long. How long are they together?

5

Leo writes 5.6 + 12 with the 12 lined up under the 5.6 like this: the 1 under the 5 and the 2 under the 6. He gets 6.8. What went wrong? What is the right answer?

Challenge

1

Jen runs 4.5 km on Monday and 3.8 km on Wednesday. Her goal for the week is 10 km. How much farther does she need to run?

2

Find the missing number: 7.6 + □ = 15.2

3

A 3 m piece of rope is cut into a 0.7 m piece, a 1.5 m piece and one more piece. How long is the last piece?

Check your understanding

Quiz

1.

What is 2.7 + 4.6?

2.

What is 9.1 − 3.5?

3.

What is 8 − 2.3?

4.

To add 14.2 + 3, how should you write the 3?

5.

A rope is 25.5 m long. An 18.5 m piece is cut off. How much is left?

6.

What is 15.8 + 6.4?

For parents and teachers

Big idea: The curriculum (B2.4) includes adding and subtracting decimal tenths with tools, strategies and algorithms. The column method works exactly like whole numbers once the decimal points are lined up.

Common difficulties:

  • Lining up the last digits instead of the decimal points (5.6 + 12). Have your child rewrite whole numbers with ".0".
  • Writing 13 tenths as ".13" instead of regrouping to 1.3.
  • Losing the decimal point in the answer. Estimating first catches this.

How to help: Use real measurements: snowfall in centimetres from the weather report, masses on food packages (kg), and distances in kilometres. Grade 4 works with tenths only; hundredths come in Grade 5.