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

Dividing Decimals by Whole Numbers

B2.11 A1About 45 minutes
Learning goals
  • I can divide decimals to thousandths by whole numbers up to 10.
  • I can estimate to place the decimal point.
  • I can keep dividing by writing placeholder zeros.
  • I can use decimal division to solve problems like sharing costs and finding unit prices.

Words to know

dividend
The number being divided.
divisor
The number you divide by.
quotient
The answer when you divide.
placeholder zero
A zero added at the end of a decimal, like 6.3 = 6.300. It doesn't change the value, but gives you more places to divide into.
unit price
The cost of one item or one unit, like $1.33 per can.

Let's start with a pizza bill

Four friends share a pizza that costs $13.80. How much does each friend pay?

Estimate first: $12 ÷ 4 = $3, and $16 ÷ 4 = $4. So each pays between $3 and $4.

Think of the money: 13 dollars and 80 cents. 12 dollars ÷ 4 = 3 dollars. That leaves 1 dollar and 80 cents = 180 cents. 180 cents ÷ 4 = 45 cents. So each friend pays $3.45.

Check: 3.45 × 4 = 13.80. ✓

A pepperoni pizza cut into eight slices on a wooden table, with four empty plates around it.
Four friends share one pizza and one bill. Dividing $13.80 by 4 tells each friend what to pay. AI-generated image
Sharing a $13.80 pizza bill four ways$13.80= $12 + $1.80$12 ÷ 4 = $3180¢ ÷ 4 = 45¢$345¢$3.45$345¢$3.45$345¢$3.45$345¢$3.45Check: 4 × $3.45 = $13.80
Share the dollars first ($3 each), then trade the leftover $1.80 for 180 cents and share those (45¢ each). Each friend pays $3.45.

Divide by place value

Dividing a decimal by a whole number is like sharing base ten blocks. You share the biggest place first, then trade what's left for the next smaller place.

7.248 ÷ 4

  • 7 ones ÷ 4 = 1 one each, with 3 ones left. Trade 3 ones for 30 tenths.
  • 30 + 2 = 32 tenths ÷ 4 = 8 tenths each. Nothing left.
  • 4 hundredths ÷ 4 = 1 hundredth each.
  • 8 thousandths ÷ 4 = 2 thousandths each.

So 7.248 ÷ 4 = 1.812.

StepOnesTenthsHundredthsThousandths
7.248 to share among 47248
Each share (3 leftover ones become 30 tenths: 32 tenths ÷ 4 = 8)1812
7.248 ÷ 4 = 1.812. Leftover ones are traded for tenths, just like base ten blocks.

Long division with decimals

You can also use long division. Write the decimal point in the quotient straight above the decimal point in the dividend. Then divide exactly like whole numbers.

If you run out of digits but still have a remainder, write a placeholder zero and keep going: 6.3 = 6.30 = 6.300.

Worked example

Example 1: Long division

9.45 ÷ 5 = ?

  1. Estimate: 10 ÷ 5 = 2. The answer is a bit less than 2.
  2. 9 ÷ 5 = 1, remainder 4. Write the decimal point above the decimal point.
  3. Bring down the 4: 44 tenths ÷ 5 = 8, remainder 4.
  4. Bring down the 5: 45 hundredths ÷ 5 = 9, remainder 0.
  5. Check: 1.89 × 5 = 9.45. ✓

9.45 ÷ 5 = 1.89

Long division: 9.45 ÷ 51.8959.45−544−4045−450point goes straight up9 ones ÷ 5 = 1, remainder 444 tenths ÷ 5 = 8, remainder 445 hundredths ÷ 5 = 9remainder 0: done!
Write the decimal point in the quotient straight above the one in 9.45, then divide just like whole numbers: 1.89.
Worked example

Example 2: Add placeholder zeros

6.3 ÷ 4 = ?

  1. Estimate: 6 ÷ 4 = 1.5. About 1.5.
  2. 6 ÷ 4 = 1, remainder 2. 23 tenths ÷ 4 = 5, remainder 3.
  3. No more digits, so write 6.3 as 6.30. 30 hundredths ÷ 4 = 7, remainder 2.
  4. Write another zero: 6.300. 20 thousandths ÷ 4 = 5, remainder 0.
  5. Check: 1.575 × 4 = 6.300. ✓

6.3 ÷ 4 = 1.575

Worked example

Example 3: A small quotient

2.736 ÷ 8 = ?

  1. Estimate: 2.736 is less than 8, so the answer is less than 1. 2.4 ÷ 8 = 0.3, so about 0.3.
  2. 2 ÷ 8 = 0. Write 0 and the decimal point.
  3. 27 tenths ÷ 8 = 3, remainder 3. 33 hundredths ÷ 8 = 4, remainder 1. 16 thousandths ÷ 8 = 2, remainder 0.
  4. Check: 0.342 × 8 = 2.736. ✓

2.736 ÷ 8 = 0.342

Estimate first

Before you divide, make an estimate so you know where the decimal point goes. If you find 9.45 ÷ 5 = 18.9, your estimate (about 2) tells you right away the decimal point is in the wrong place.

Just for fun

Sharing a $13.80 pizza bill four ways is easy: $3.45 each. Sharing the last slice four ways? That's the real math challenge.

Hands-on activity

Average apple

You need: a kitchen scale that shows grams, a bag of apples (or potatoes, oranges or onions), paper, a pencil and a calculator for checking.

  1. Put 6 apples on the scale together. Write the mass in kilograms with three decimal places. (For example, 1 074 g = 1.074 kg.)
  2. Estimate the mass of one apple.
  3. Divide the total by 6 using long division. This is the average (mean) mass of one apple.
  4. Weigh one apple by itself. Is it close to your answer? Why might it be a bit different?
  5. Try again with a different number of items (up to 10).

Math talk: "How did you know where to put the decimal point?"

Your turn

1

6.9 ÷ 3 = ?

2

4.8 ÷ 6 = ?

3

9.36 ÷ 4 = ?

4

5.625 ÷ 5 = ?

5

7.2 ÷ 8 = ?

6

3.5 ÷ 2 = ?

7

12.474 ÷ 9 = ?

More practice: warm-up

1

0.8 ÷ 2 = ?

2

0.9 ÷ 3 = ?

3

2.4 ÷ 4 = ?

4

1.5 ÷ 5 = ?

5

0.036 ÷ 6 = ?

More practice: on your own

1

8.52 ÷ 6 = ?

2

4.375 ÷ 7 = ?

3

9.1 ÷ 2 = ?

4

Six friends share a $25.50 bill equally. How much does each pay?

5

3.048 ÷ 8 = ?

Challenge

1

A relay team of 4 runners finishes in 58.36 s. If each runner took the same time, how long was each leg?

2

Store A sells 6 cans of juice for $7.98. Store B sells 4 cans for $5.40. Which is the better buy? Use unit prices.

3

A 1.5 km cross-country ski trail is split into 6 equal sections. How long is each section, in kilometres and in metres?

Check your understanding

Quiz

1.

What is 8.4 ÷ 2?

2.

What is 3.6 ÷ 9?

3.

What is 7.25 ÷ 5?

4.

What is the best estimate for 23.88 ÷ 6?

5.

What is 5.1 ÷ 4?

6.

You are dividing 6.3 ÷ 4 and you have a remainder after the tenths. What should you do?

For parents and teachers

Big idea: B2.11 asks Grade 6 students to represent and solve problems involving the division of decimal numbers up to thousandths by whole numbers up to 10, using appropriate tools and strategies. Sharing by place value (like base ten blocks or money) explains why long division works, and estimating tells you where the decimal point goes.

Common difficulties:

  • Misplacing the decimal point. Write it in the quotient straight above the one in the dividend, and estimate.
  • Forgetting a 0 in the quotient (like 0.036 ÷ 6 = 0.006, not 0.6).
  • Stopping with a remainder instead of adding placeholder zeros.

How to help: Share real bills and costs: "The groceries were $27.48 for 4 days. How much per day?" Compare unit prices at the store. Ask your child to explain how they knew where the decimal point goes; this builds the A1 skill of communicating and reasoning.