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

7.09 Divide decimals by whole numbers

Lesson

Practice

7.10 Story problems with multiplication or division

7.11 Value of decimal expressions

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Australia

Year 6

7.09 Divide decimals by whole numbers

Lesson

Practice

Lesson

Are you ready?

In previous lessons we have learned how to divide whole numbers by using short division . Let's review by looking to the following example.

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 decimal by a 1 digit number

This video uses a model to show how we can use regrouping to divide the total into groups. Then we use the same example and solve using the algorithm.

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Examples

Example 2

Find the value of 92.4\div6.

Worked Solution

Create a strategy

Use short division.

Apply the idea

92.4 divided by 6 in a short division algorithm. Ask your teacher for more information.

6 goes into 9 once with 3 remaining, so we put a 1 in the tens column at the top and carry 3 to the units column.

6 goes into 32 five times with 2 remaining, so we put a 5 in the units column at the top and carry 2 to the tenths column.

6 goes into 24 four times with 0 remaining, so we put a decimal point and a 4 in the tenths column at the top.

92.4\div6=15.4

Idea summary

Dividing a decimal using short division is the same process as dividing a whole number. We just need to remember to include the decimal point in the answer.

Divide a decimal by partitioning

This video starts by partitioning the number and then connects this process to short division.

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Examples

Example 3

Find the value of 8.904\div8.

Worked Solution

Create a strategy

Use short division.

Apply the idea

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

Set up the short division.

8 goes into 8 once with 0 remaining, so we put a 1 in the units column at the top.

8 goes into 9 once with 1 remaining, so we copy the decimal point and put a 1 in the tenths column at the top and the carry 1 to the hundredths column.

8 goes into 10 once with 2 remaining, so we put a 1 in the hundredths column at the top and carry 2 into the thousandths column.

8 goes into 24 three times with 0 remaining, so we put a 3 in the thousandths column at the top.

8.904\div8=1.113

Idea summary

When you are dividing, you always start with the digit that is farthest to the left, then continue to divide each digit to the right moving across the decimal to units, tenths and so on if necessary. 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

AC9M6N06

multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts; using estimation and rounding to check the reasonableness of answers

7.09 Divide decimals by whole numbers

Ideas

Are you ready?

Examples

Example 1

Divide a decimal by a 1 digit number

Examples

Example 2

Divide a decimal by partitioning

Examples

Example 3

Outcomes

AC9M6N06

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