7. Decimal operations

7.02 Subtract decimals

7.03 Add and subtract to thousandths

7.04 Story problems with addition and subtraction

7.05 Powers of 10

7.06 Multiply decimals by single digit numbers

7.07 Multiply decimals by whole numbers

7.08 Division where answers are decimals

Lesson

Practice

7.09 Divide decimals by whole numbers

7.10 Story problems with multiplication or division

7.11 Value of decimal expressions

Book a Demo

Australia NSW

Stage 3

7.08 Division where answers are decimals

Lesson

Practice

Lesson

Ideas

Are you ready?
Divide a 3 digit number by a 1 digit number
Short division
Divide a 4 digit number by a 2 digit number

Are you ready?

We've previously learned how to use a division algorithm with short division . Let's practice this concept.

Examples

Example 1

Find the value of 856\div8.

Worked Solution

Create a strategy

Use short division.

Apply the idea

856 divided by 8 in a short division algorithm. Ask your teacher for more information.

Set up the short division.

8 goes into 8 once, so we put a 1 in the hundreds place at the top.

8 goes into 5 zero times with 5 remaining, so we put a 0 in the tens place at the top and carry the 5 to the units column.

8 goes into 56 seven times, so we put a 7 in the units column.

856 \div 8 = 107

Idea summary

We can use short division to divide one number by another. We start dividing at the highest place value and carry any remainders to the next place value.

Divide a 3 digit number by a 1 digit number

Sometimes when we divide whole numbers there is a remainder, this remainder can be expressed as a decimal. This video will show us how.

Loading video...

Examples

Example 2

Find the value of 460\div8.

Worked Solution

Create a strategy

Use short division.

Apply the idea

A short division with 460 being divided by 8. Ask your teacher for more information

Set up the short division.

8 can fit into 4 zero times with 4 remaining, so we put 0 on the hundreds place at the top and carry the 4 to the tens column.

8 can fit into 46 five times with 6 remaining, so we put 5 in the tens place at the top and carry the 6 to the units column.

8 can fit into 60 seven times with 4 remaining, so we put 7 in the units place at the top.

We have run our of digits to carry the remainder to, so we need to a decimal point and a 0 in the tenths place. Now we can carry the 4 to the tenths column.

8 can fit into 40 five times with 0 remaining, so we put 5 in the tenths place at the top.

There are no more digits to divide by 8, so we know that we are finished.

460\div8=57.5

Idea summary

When dividing a whole number using short division, if we have a remainder after dividing the units place we will end up with a decimal answer.

Short division

This video looks at short division and how to use short division when there is a remainder.

Loading video...

Examples

Example 3

Find the value of 3653\div4.

Worked Solution

Create a strategy

Use short division.

Apply the idea

A short division with 3653 being divided by 4. Ask your teacher for more information

Set up the short division.

4 fits into 36 nine times with 0 remaining, so we put 9 in the hundreds place at the top.

4 fits into 5 once with 1 remaining, so we put 1 in the tens place at the top and carry 1 to the units column.

4 fits into 13 three times with 1 remaining, so we put 3 in the units place at the top.

Since we have a remainder, we add a decimal point and a 0 in the tenths place and carry 1 to the tenths column.

4 fits into 10 two times with 2 remaining, so we put 2 in the tenths place at the top.

We add a 0 in the hundredths place and carry the 2 to the hundredths column.

4 fits into 20 five times with 0 remaining, so we put 5 in the hundredths place at the top.

There are no more digits to divide by 4, so we know that we are finished.

3653\div4=913.25

Idea summary

When dividing a whole number using short division, if we have a remainder, we can add a decimal point and add 0s after the decimal point to carry the remainders to until there are no more remainders.

Divide a 4 digit number by a 2 digit number

This video looks at how to divide by a two digit number using short division. By remembering place value, we can divide each digit, working from left to right. We move from units to tenths and so on if necessary.

Loading video...

Examples

Example 4

Find the value of 460\div25.

Worked Solution

Create a strategy

Use short division.

Apply the idea

A long division with 460 being divided by 25. Ask your teacher for more information

Set up the short division.

25 fits into 4 zero times so we put a 0 above the 4. \,\, 25 fits into 46 once, so we put 1 in the tens place at the top.

25\times 1=25 and 46-25=21 so we have a remainder of 21 which we carry to the units column.

25 fits into 210 eight times since 25\times 8 =200. So we put 8 in the units place at the top and carry 10 to the tenths column by adding a decimal point and a 0.

25 fits into 100 four times, so we put 4 in the units place at the top.

There are no more digits to divide by 25, so we know that we are finished.

460\div25=18.4

Idea summary

When you are dividing, you always start with the digit that is farthest to the left. If you get to a digit that you can't divide into, make sure you put a placeholder zero in the answer, before moving to the next digit.

Outcomes

MA3-6NA

selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

7.08 Division where answers are decimals

Ideas

Are you ready?

Examples

Example 1

Divide a 3 digit number by a 1 digit number

Examples

Example 2

Short division

Examples

Example 3

Divide a 4 digit number by a 2 digit number

Examples

Example 4

Outcomes

MA3-6NA

MA3-7NA

What is Mathspace

About Mathspace