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

Mental Math: Adding and Subtracting Tenths

B2.3 A1About 35 minutes
Learning goals
  • I can add and subtract decimal tenths in my head.
  • I can make a whole number to add tenths.
  • I can count up to subtract tenths.
  • I can explain the strategy I used.

Words to know

tenth
One of 10 equal parts of a whole. Written 0.1 or 1/10.
decimal point
The dot that separates the whole number from the tenths, like in 2.4.
decimal number
A number with a decimal point, like 3.7 (3 wholes and 7 tenths).
compensate
Change a number to make it friendly, then fix the answer.

Tenths: a quick reminder

When a whole is cut into 10 equal parts, each part is one tenth. We write one tenth as 0.1 (or 1/10).

  • 0.4 means 4 tenths.
  • 10 tenths make 1 whole: 1.0 = 1.
  • 2.6 means 2 wholes and 6 tenths.
00.511.52
A number line from 0 to 2 with a tick for every tenth. The dots are at 0.4, 1 and 1.6.

Strategy 1: Count the tenths

Add or subtract tenths just like ones. Say the word "tenths" to help.

  • 0.3 + 0.4 → 3 tenths + 4 tenths = 7 tenths = 0.7
  • 0.9 − 0.5 → 9 tenths − 5 tenths = 4 tenths = 0.4

Strategy 2: Make a whole

When the tenths add up to 10 or more, make a whole first, just like making 10 with ones.

Worked example

Example 1: Make a whole

Solve 0.6 + 0.7.

  1. 0.6 needs 0.4 more to make 1.
  2. Split 0.7 into 0.4 + 0.3.
  3. 0.6 + 0.4 = 1.
  4. 1 + 0.3 = 1.3.

0.6 + 0.7 = 1.3. (6 tenths + 7 tenths = 13 tenths = 1 whole and 3 tenths.)

00.511.52+0.4+0.3
Start at 0.6. Jump 0.4 to make 1. Then jump 0.3 more to 1.3.

Strategy 3: Wholes first, then tenths

Split the numbers into wholes and tenths.

2.4 + 3.5: wholes 2 + 3 = 5. Tenths 0.4 + 0.5 = 0.9. Together: 5.9.

Worked example

Example 2: Use a whole number and fix it

Solve 4.9 + 2.3.

  1. 4.9 is just 0.1 less than 5.
  2. Add 5 instead: 5 + 2.3 = 7.3.
  3. We added 0.1 too much, so take it away: 7.3 − 0.1 = 7.2.

4.9 + 2.3 = 7.2

Worked example

Example 3: Count up to subtract

Solve 3.2 − 2.8.

  1. The numbers are close, so count up from 2.8.
  2. 2.8 + 0.2 = 3.
  3. 3 + 0.2 = 3.2.
  4. Add the jumps: 0.2 + 0.2 = 0.4.

3.2 − 2.8 = 0.4

2.533.5+0.2+0.2
Count up from 2.8: jump 0.2 to 3, then 0.2 more to 3.2. The jumps add to 0.4.

Where do we see tenths?

  • A carton of juice holds 1.5 L.
  • A walk to school might be 0.8 km.
  • A dime is one tenth of a dollar. Ten dimes make one loonie.

Math talk

There is more than one good way to solve 4.9 + 2.3. After each question, explain your strategy: "I made a whole" or "I added 5 and took away a tenth." Then listen to your grown-up's way. Comparing ways helps you pick the fastest one next time.

Just for fun

A snail sliding 0.1 m at a time needs 10 slides to travel just 1 metre. Slow and steady adds up the tenths!

Hands-on activity

Dimes and loonies

You need: 1 or 2 loonies and about 20 dimes (or paper circles marked "0.1" and "1").

A dime is one tenth of a dollar, so it can stand for 0.1. A loonie stands for 1.

  1. Show 0.7 with 7 dimes and 0.6 with 6 dimes.
  2. Push them together. Can you trade 10 dimes for 1 loonie? You have 1 loonie and 3 dimes: 1.3.
  3. Your grown-up says a question, like 1.4 + 0.8 or 2.0 − 0.6. Solve it with the coins, then say your answer and strategy.
  4. Try the next three questions in your head first, then check with coins.

Math talk: "How is trading 10 dimes for a loonie like trading 10 ones for a ten?"

Your turn

1

0.3 + 0.5 = ?

2

0.9 − 0.4 = ?

3

0.7 + 0.6 = ?

4

2.4 + 1.3 = ?

5

5 − 0.2 = ?

6

3.9 + 1.4 = ?

7

4.1 − 3.8 = ?

More practice: warm-up

1

0.2 + 0.2 = ?

2

0.5 + 0.5 = ?

3

0.8 − 0.3 = ?

4

1 + 0.6 = ?

5

0.4 + 0.6 = ?

More practice: on your own

1

1.8 + 0.5 = ?

2

6.3 − 0.5 = ?

3

2.9 + 2.9 = ?

4

7.2 − 1.9 = ?

5

Maya skis 1.5 km on Saturday and 2.5 km on Sunday. How far in all?

Challenge

1

Find the missing number: 3.6 + □ = 5

2

A jug holds 2 L of water. Sam pours out 0.8 L, then 0.7 L. How much is left?

3

Sam says 0.6 + 0.5 = 0.11. Explain the mistake.

Check your understanding

Quiz

1.

What is 0.4 + 0.5?

2.

What is 0.8 + 0.4?

3.

What is 3 − 0.1?

4.

What is 2.5 + 1.5?

5.

What is 5.2 − 4.9?

6.

How many tenths make 1 whole?

For parents and teachers

Big idea: The curriculum (B2.3) asks Grade 4 students to add and subtract decimal tenths mentally and to explain their strategies. The key idea is that 10 tenths make 1 whole, just as 10 ones make a ten.

Common difficulties:

  • Treating the decimal as two separate numbers (0.6 + 0.5 = 0.11). Have your child say "6 tenths plus 5 tenths is 11 tenths" and trade 10 tenths for a whole.
  • Thinking 0.10 is bigger than 0.9. In Grade 4, keep to tenths and use dimes or a number line to compare.
  • Fixing a friendly-number answer the wrong way. Ask: "Did you add too much or too little?"

How to help: Use dimes and loonies, distances on signs (2.5 km), and litres on drink containers. Mental math is about flexible thinking; encourage your child to explain, and share your own strategy too (A1: communicating and reflecting).