Math Core

Four friends share a $7.00 pizza bill equally. A 3-meter board is cut into pieces that are each 0.5 meter long. Both situations call for dividing with decimals. Division asks one of two questions: how much goes in each group, or how many groups fit. Decimals don't change those questions. You just need to keep track of place value.

A decimal divided by a whole number

Think of the decimal in place value units. $0.8 \div 4$ means 8 tenths shared into 4 equal groups. Each group gets 2 tenths, so

0.8 \div 4 = 0.2

For bigger numbers, use long division. Divide exactly as you would with whole numbers, and put the decimal point in the quotient straight above the decimal point in the dividend.

Worked example: Long division with a decimal

Find $7.35 \div 3$ .

Ones: $7 \div 3 = 2$ with 1 left over. Write 2 in the ones place.
Decimal point: Write the decimal point in the quotient right above the one in 7.35.
Tenths: The leftover 1 one is 10 tenths. Add the 3 tenths to get 13 tenths. $13 \div 3 = 4$ with 1 left over. Write 4 in the tenths place.
Hundredths: The leftover 1 tenth is 10 hundredths. Add the 5 hundredths to get 15 hundredths. $15 \div 3 = 5$ . Write 5 in the hundredths place.

So $7.35 \div 3 = 2.45$ . Check: $3 \times 2.45 = 7.35$ .

Writing extra zeros

Sometimes there is a remainder when you run out of digits. Remember that zeros at the end of a decimal don't change its value: $6.6 = 6.60$ . Write a zero and keep dividing.

Worked example: Keep going with a zero

Four friends split a $5.40 snack bill equally. How much does each friend pay?

Find $5.40 \div 4$ .

Ones: $5 \div 4 = 1$ with 1 left over.
Tenths: 1 one is 10 tenths, plus 4 tenths is 14 tenths. $14 \div 4 = 3$ with 2 left over.
Hundredths: 2 tenths is 20 hundredths, plus the 0 hundredths is 20. $20 \div 4 = 5$ .

So $5.40 \div 4 = 1.35$ . Each friend pays $1.35. Check: $4 \times 1.35 = 5.40$ .

Dividing by a decimal

Now the divisor is a decimal. Use the "how many groups fit" question. $3 \div 0.5$ asks: how many halves are in 3? Each whole has 2 halves, so 3 wholes have 6 halves.

3 \div 0.5 = 6

The answer is bigger than 3. That is normal: when you divide by a number less than 1, lots of small pieces fit.

A handy trick is to change the problem into one with a whole-number divisor. If you multiply both numbers by the same power of ten, the quotient stays the same. It's like asking how many 5-dime piles you can make from 30 dimes instead of how many half dollars fit in 3 dollars.

3 \div 0.5 = 30 \div 5 = 6

Dividing by a decimal

Multiply the divisor by 10 or 100 to make it a whole number.
Multiply the dividend by the same number.
Divide. The quotient is the same as the original problem's.

Worked example: Make the divisor whole

Find $4.8 \div 0.6$ and $1.2 \div 0.04$ .

First problem. Multiply both numbers by 10: $4.8 \div 0.6 = 48 \div 6 = 8$ .

Check: $8 \times 0.6 = 4.8$ .

Second problem. The divisor has hundredths, so multiply both numbers by 100: $1.2 \div 0.04 = 120 \div 4 = 30$ .

Check: $30 \times 0.04 = 1.20$ .

Common mistake

Change both numbers, not just the divisor. For $4.8 \div 0.6$ , changing only the divisor gives $4.8 \div 6 = 0.8$ , which is ten times too small. Always check by multiplying: $0.8 \times 0.6 = 0.48$ , not 4.8, so 0.8 can't be right.

Tip

Estimate first. $7.35 \div 3$ is about $6 \div 3 = 2$ , so an answer near 2 makes sense. If you got 24.5 or 0.245, you'd know the decimal point was in the wrong place.

Practice

Practice 1

Find $0.9 \div 3$ .

Type a number.

Practice 2

Find $8.4 \div 4$ .

Type a number.

Practice 3

Find $9.36 \div 4$ .

Type a number.

Practice 4

Find $6.6 \div 4$ .

Type a number.

Practice 5

Find $4 \div 0.5$ .

Type a number.

Practice 6

Find $3.6 \div 0.4$ .

Type a number.

Practice 7

What is $1.5 \div 0.05$ ?

Practice 8

Five friends share the cost of a gift equally. The gift costs $18.25. How much does each friend pay, in dollars?

Type a number.