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

Adding and Subtracting Decimals to Hundredths

B2.4 B2.1About 45 minutes
Learning goals
  • I can show adding and subtracting hundredths on a hundredths grid.
  • I can line up decimal points to add and subtract decimals up to hundredths.
  • I can regroup 10 hundredths as 1 tenth, and 10 tenths as 1 whole.
  • I can solve money and measurement problems with decimals.

Words to know

decimal point
The dot that separates the whole number part from the parts smaller than one.
hundredth
One of 100 equal parts of a whole. 0.01 is one hundredth.
placeholder zero
A zero you write to fill an empty place, like writing 12.5 as 12.50, so the digits line up.

Remember from Grade 4

In Grade 4 you added and subtracted tenths, like 16.4 + 8.9, by lining up the decimal points and regrouping 10 tenths as 1 whole. In Grade 5 you'll work with hundredths too. Money is a great example: $4.56 means 4 dollars and 56 hundredths of a dollar (56 cents).

Let's start with a hundredths grid

A hundredths grid is one whole cut into 100 equal squares. Each square is 0.01. Each column of 10 squares is 0.1.

Shade 0.35 in one colour (3 columns and 5 squares). Then shade 0.48 more in another colour (4 columns and 8 squares).

How much is shaded? 0.35 + 0.48 = 0.83.

A hundredths grid. 35 squares are shaded blue and 48 more squares are shaded yellow. 35 + 48 = 83 squares, so 0.35 + 0.48 = 0.83.

The column method for decimals

  1. Line up the decimal points. Then every digit is in its right place: ones under ones, tenths under tenths, hundredths under hundredths.
  2. If one number has fewer decimal places, write placeholder zeros (12.5 = 12.50).
  3. Add or subtract from the right, just like whole numbers. Regroup when you need to.
  4. Put the decimal point in the answer straight below the others.
1165.487.2+43.7
4.56 + 2.78 = 7.34. The decimal points are lined up. The small 1s show regrouping: 10 hundredths make 1 tenth, and 10 tenths make 1 whole.
Worked example

Example 1: Add hundredths

Solve 4.56 + 2.78.

  1. Line up the decimal points.
  2. Hundredths: 6 + 8 = 14 hundredths. Write 4, regroup 10 hundredths as 1 tenth.
  3. Tenths: 1 + 5 + 7 = 13 tenths. Write 3, regroup 10 tenths as 1 whole.
  4. Ones: 1 + 4 + 2 = 7.
  5. Estimate to check: 5 + 3 = 8. 7.34 is close. ✓

4.56 + 2.78 = 7.34

Worked example

Example 2: Different numbers of decimal places

Solve 12.5 + 3.47.

  1. Write 12.5 as 12.50 so both numbers have hundredths.
  2. Hundredths: 0 + 7 = 7. Tenths: 5 + 4 = 9. Ones: 2 + 3 = 5. Tens: 1.

12.5 + 3.47 = 15.97

Worked example

Example 3: Subtract with regrouping

Solve 8.03 − 2.76.

  1. Hundredths: 3 − 6? Not enough. The tenths digit is 0, so go to the ones.
  2. Take 1 whole from 8 (7 are left) and trade it for 10 tenths. Take 1 tenth (9 are left) and trade it for 10 hundredths: 13 hundredths.
  3. Hundredths: 13 − 6 = 7. Tenths: 9 − 7 = 2. Ones: 7 − 2 = 5.
  4. Check with addition: 5.27 + 2.76 = 8.03. ✓

8.03 − 2.76 = 5.27

Worked example

Example 4: Making change

You pay for a $13.47 book with a $20 bill. How much change do you get?

  1. Count up from 13.47: + 0.03 makes 13.50. + 0.50 makes 14.00. + 6.00 makes 20.00.
  2. Add the jumps: 0.03 + 0.50 + 6.00 = 6.53.
  3. Or use the column method: 20.00 − 13.47 = 6.53.

$6.53 in change

Watch out!

The most common decimal mistake is lining up the last digits instead of the decimal points. 5.6 + 2.35 is not 2.91! Line up the points: 5.60 + 2.35 = 7.95. An estimate (6 + 2 = 8) tells you right away that 2.91 can't be right.

Just for fun

Riddle: Why did the decimal point always get picked first for the team photo?

Because it knows exactly how to line up!

Hands-on activity

Standing long jump

You need: a measuring tape or metre stick, a piece of masking tape for a start line, and a safe, clear space (outside on grass is best, or a carpeted floor with nothing to trip on). A grown-up should be nearby.

  1. Stand behind the start line. Jump forward with both feet together.
  2. Measure from the line to the back of your heels, in centimetres. Change it to metres (for example, 124 cm = 1.24 m).
  3. Jump 3 times. Add your two best jumps.
  4. Find the difference between your longest and shortest jumps.
  5. If a grown-up jumps too, find how much farther one jump was than the other.

Math talk: "Why do we line up the decimal points when we subtract?"

Your turn

1

3.25 + 4.61 = ?

2

5.48 + 2.67 = ?

3

9.72 − 3.41 = ?

4

6.05 − 2.38 = ?

5

7.4 + 1.86 = ?

6

15 − 6.28 = ?

7

Lunch costs $4.75 and milk costs $1.35. What is the total?

More practice: warm-up

1

0.3 + 0.4 = ?

2

0.25 + 0.5 = ?

3

1.50 + 1.50 = ?

4

0.9 − 0.2 = ?

5

2.75 − 0.25 = ?

More practice: on your own

1

23.67 + 18.95 = ?

2

40.1 − 12.84 = ?

3

Ava jumped 1.36 m. Ben jumped 1.18 m. How much farther did Ava jump?

4

Find the total cost: $2.49, $5.75 and $0.89.

5

Leo wrote 5.6 + 2.35 = 2.91. What did he do wrong? What is the right answer?

Challenge

1

You pay for items costing $18.65 and $24.79 with a $50 bill. How much change do you get?

2

Find the missing number: 3.48 + □ = 10.

3

Snowfalls this week were 4.25 cm, 3.8 cm and 6.15 cm. How much more snow is needed to reach 20 cm for the week?

Check your understanding

Quiz

1.

What is 2.45 + 3.38?

2.

What is 7.2 − 3.65?

3.

When you add decimals in columns, what must you line up?

4.

You pay $10 for something that costs $6.45. What is your change?

5.

What is 0.6 + 0.25?

6.

What is 12.08 + 3.9?

For parents and teachers

Big idea: The Grade 5 curriculum (B2.4) includes adding and subtracting decimal numbers up to hundredths. Students should understand why we line up the decimal points (to match place values) and be able to regroup 10 hundredths as 1 tenth.

Common difficulties:

  • Lining up the last digits instead of the decimal points. Have your child write placeholder zeros so both numbers have the same number of decimal places.
  • Forgetting the decimal point in the answer.
  • Regrouping across a zero (8.03 − 2.76). Use money: trade a loonie for 10 dimes, and a dime for 10 cents.

How to help: Money is the best tool here. Let your child total a few items on a receipt, or work out the change when you pay. Measuring in metres and centimetres works well too.