Grade 6

2.11 Divide decimals

Introduction

In this lesson we will look at dividing with decimals. We will look at methods for solving problems including dividing decimal numbers by whole numbers, and dividing decimals by decimals.

Ideas

Divide with decimals
Divide by a decimal number

Divide with decimals

This video shows how we can use long division to divide numbers with decimals, the same way that we would for whole numbers. It also shows how we can use estimation to check the position of the decimal point.

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Examples

Example 1

Find the value of 68.4 \div 6.

Worked Solution

Create a strategy

Use long division.

Apply the idea

A long division where 68.4 is the dividend and 6 is the divisor. Ask your teacher for more information.

Setup the long division. Remember to keep the decimal points aligned.

6 divided by 6 is 1. So we put 1 in the tens place at the top.

Multiply 1 by 6 to get 6 and write this under the previous 6.

Subtract 6 from 6 to get 0.

Since 6 does not fit into 0 we need to bring down 8 from the ones place.

6 fits into 8 once so we write 1 in the ones place at the top.

Multiply 1 by 6 to get 6 and write this under 8.

Subtract 6 from 8 to get 2.

6 does not fit into 2 so we need to bring down the 4 in the tenths place to make 24.

24 divided by 6 is 4. So we put 4 in the tenths place at the top.

Multiply 4 by 6 to get 24 and write this under the previous 24.

Subtract 24 from 24 to get 0.

68.4 \div 6 = 11.4

Idea summary

When we are dividing, we 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.

The place values of the number being divided and the result of the division should line up.

Divide by a decimal number

But what about when we want to divide by a decimal number?

We've already seen how to divide decimal numbers by whole numbers, so it would be great if we could just keep using this strategy. Using our knowledge of place value, we can.

We know that 10\div5=2, but what is 100\div50? Well, obviously that is just 2 as well. We can see that even though both numbers were ten times larger, we ended up with exactly the same answer. We can use the same strategy but with numbers ten times smaller. This means 1\div0.5=2 as well.

Remember: To divide a decimal by a decimal, we can first multiply both numbers by a suitable power of 10 to make them whole numbers. This can make the division more efficient.

Examples

Example 2

Evaluate the quotient 1.2\div0.3

Worked Solution

Create a strategy

Multiply both numbers by a power of 10 to make them whole numbers.

Apply the idea

\displaystyle 1.2\div0.3	\displaystyle =	\displaystyle (1.2\times10)\div(0.3\times10)	Multiply both decimal numbers by 10
	\displaystyle =	\displaystyle 12\div3	Evaluate multiplication
	\displaystyle =	\displaystyle 4	Evaluate division

Example 3

Evaluate 5.289\div0.04

Worked Solution

Create a strategy

Multiply both numbers by a power of 10 to make them whole numbers, then use long division to find the quotient.

Apply the idea

\displaystyle 5.289\div0.04	\displaystyle =	\displaystyle (5.289\times100)\div(0.04\times100)	Multiply both decimal numbers by 100
	\displaystyle =	\displaystyle 528.9\div4

Now we can long division.

Divide 5 by 4. There is 1 four in 5, so we write 1 in the hundreds place above the 5.

Multiply 1 by 4 to get 4 and write this under the 5.

A long division where 528.9 is the dividend and 4 is the divisor. Ask your teacher for more information.

Subtract 4 from 5 to get 1 and bring down the 2 from the tens place so we have 12.

Divide 12 by 4 . There are 3 fours in 12 so we write 3 above the 2 in the tens place.

Multiply 3 by 4 and write 12 under the previous 12.

Subtract 12 from 12 to get 0 and bring down 8 from the ones place.

Divide 8 by 4. There are 2 fours in 8, so 2 will go above the 8 in the ones place.

Multiply 2 by 4 and write this under the previous 8.

Subtract 8 from 8 to get 0 .

Bring down the 9 from the tenths place.

Divide 9 by 4. There are 2 fours in 9 so put the 2 above the 9 in the tenths place.

Multiply 2 by 4 to get 8 and write this under the9 that was brought down.

Subtract 8 from 9 to get 1 . We can still continue dividing by adding 0 to the dividend then bring down 0 beside 1.

Divide 10 by 4. There are 2 fours in 10 so put the 2 above the 0 in the hundredths place.

Multiply 2 by 4 to get 8 and write this under the 0 that was brought down.

Subtract 8 from 10 to get 2 . We can still continue dividing by adding 0 to the dividend then bring down 0 beside 2.

Divide 20 by 4. There are 5 fours in 20 so put the 5 above the 0 in the thousandths place.

Multiply 5 by 4 to get 20 and write this under the previous 20.

Subtract 20 from 20 to get 0 . We can now stop long division as we have reached a remainder of0.

Since the last difference is 0 and that there is no need to bring down another zero, the quotient is 132.225.

Idea summary

To divide a decimal by a decimal, we can first multiply both numbers by a suitable power of 10 to make the divisor a whole number and then use long division.

Outcomes

6.NS.B.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

2.11 Divide decimals

Introduction

Ideas

Divide with decimals

Examples

Example 1

Divide by a decimal number

Examples

Example 2

Example 3

Outcomes

6.NS.B.3

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