# Divide numbers with decimals by a double digit number

Lesson

## Strategies we might use

When we divide by two digit numbers, we can use the same strategies we use with whole numbers. The decimal point tells us the value of our digits, but we can still divide them in the same way.

### Dividing by multiples of 10

You might break your number down into parts, so instead of dividing $168.48$168.48 by $20$20, you might divide it by $2$2, and then divide it by $10$10. Dividing by $2$2 allows you to work out half of your number, and dividing by $10$10 means you move each digit to the right one place. Each digit has a value $10$10 times lower when we divide by $10$10. We can use this approach anytime we are dividing by a multiple of $10$10.

This first video takes you through an example of dividing by a multiple of $10$10.

### Other strategies

If you know how to solve $360$360 divided by $36$36, using the fact we have $36$36 hundreds, divided by $36$36, which equals $100$100, you are able to take the next step to solve something like $360.72$360.72 divided by $36$36.

Let's work through a similar example in our second video. We start by estimating our answer, then we use place value to solve it, and at the end, we check our answer is correct.

### Short division

Using the two problems we've solved above, we can now try our hand at short division. We've looked at this when dividing by one digit numbers, so this is just a variation of that. By having the answer already, we can use this to guide us as we work through short division. This allows us to try it out with the ability to see if we are on the right track as we work through our problem.

This third video takes you through both examples, using short division. Did you know you could also use long division to divide decimals by two digit numbers? It's similar to short division, but you show all of your workings down the page.

Careful!

You'll see we have $10$10 units left in one of our examples, and we rename them as tenths. If we divide by a one digit number we don't need to do this, but we do here because we are dividing by a two digit number.

#### Examples

##### Question 1

We want to find $9.87\div47$9.87÷​47

1. Choose the most reasonable estimate for $9.87\div47$9.87÷​47

Between $10$10 and $100$100

A

Between $1$1 and $10$10

B

Less than $0$0

C

Between $0$0 and $1$1

D
2. Complete the multiplication table showing the first $9$9 multiples of $47$47.

 $1$1 $47$47 $2$2 $94$94 $3$3 $\editable{}$ $4$4 $\editable{}$ $5$5 $\editable{}$ $6$6 $\editable{}$ $7$7 $329$329 $8$8 $\editable{}$ $9$9 $\editable{}$
3. Complete the short division to find $9.87\div47$9.87÷​47

 $\editable{}$ $.$. $\editable{}$ $\editable{}$ $47$47 $9$9 $.$. $8$8 $\editable{}$ $7$7

##### QUESTION 2

We want to find $51.87\div21$51.87÷​21

1. Choose the most reasonable estimate for $51.87\div21$51.87÷​21

Between $1$1 and $10$10

A

Less than $0$0

B

Between $0$0 and $1$1

C

Greater than $10$10

D
2. Complete the multiplication table showing the first $9$9 multiples of $21$21.

 $1$1 $21$21 $2$2 $42$42 $3$3 $\editable{}$ $4$4 $\editable{}$ $5$5 $\editable{}$ $6$6 $\editable{}$ $7$7 $147$147 $8$8 $\editable{}$ $9$9 $\editable{}$
3. Complete the short division to find $51.87\div21$51.87÷​21

 $\editable{}$ $.$. $\editable{}$ $\editable{}$ $21$21 $5$5 $1$1 $.$. $\editable{}$ $8$8 $\editable{}$ $7$7

##### QUESTION 3

We want to find $331.89\div23$331.89÷​23

1. Choose the most reasonable estimate for $331.89\div23$331.89÷​23

Between $100$100 and $1000$1000

A

Between $1$1 and $10$10

B

Between $10$10 and $100$100

C

Between $0$0 and $1$1

D
2. Complete the multiplication table showing the first $9$9 multiples of $23$23.

 $1$1 $23$23 $2$2 $46$46 $3$3 $\editable{}$ $4$4 $\editable{}$ $5$5 $\editable{}$ $6$6 $\editable{}$ $7$7 $161$161 $8$8 $\editable{}$ $9$9 $\editable{}$
3. Complete the short division to find $331.89\div23$331.89÷​23

 $\editable{}$ $\editable{}$ $.$. $\editable{}$ $\editable{}$ $23$23 $3$3 $3$3 $\editable{}$ $1$1 $.$. $\editable{}$ $8$8 $\editable{}$ $9$9

### Outcomes

#### NA5-3

Understand operations on fractions, decimals, percentages, and integers