Rates of Change

I am learning to solve rate problems.

You can buy 16 apples for $12. How many apples can you buy for $9?

There are a few different ways we can work this out. First lets try using pictures.

apples

$1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 $1 Dollars

You can see it takes $3 to buy 4 apples

If you can buy 4 apples for $3 you must be able to buy 12 apples for $9

Dollars Apples

$3 4

$6 8

$9 12

$12 16

Now let’s use a table to answer the same question.

You can buy 16 apples for $12. How many apples can you buy for $9?

Dollars Apples

$12 16

$9 …..

Divide the $12 by 4 so we can work out how many Apples we will get for $3

Divide the 16 by 4 so we can work out how many Apples we will get for $3

Note: I chose to divide by 4 because I knew both numbers (12 and 16) are divisible by 4.

$3 4

To change $3 into $9 I must multiply by three. That means I must also multiply the number of apples by three.

$12

A bottling machine can fill 24 bottles very 60 seconds. How many can it fill every 15 seconds?

Seconds Bottles

60 seconds 24 bottles

15 seconds ….. bottles

15 seconds is of 60 seconds 60

15

We can simplify that to . 4

1

So of 60 is 15 seconds. That’s the same as saying 60 ÷ 4 = 154

1

÷ 4

So if we divide 24 by 4 we will find how many bottles can be filled in 60 seconds.

6÷ 4

Seconds Bottles

60 seconds 24 bottles

15 seconds ….. bottles

We solved the last question by using a ‘within’ strategy. Identifying how the 60 seconds was changed into 15 seconds.

Now we are going to answer the same problem using a ‘between’ strategy (comparing the 60 seconds to the 24 bottles).

24 is of 60.

60

24We can simplify this to

5

2

So of 60 is 24. That’s the same as saying 60 ÷ 5 =12 then multiplying this by 2 because we have two fifths, not one fifth.

5

2

5

2

Now we need to find of 15.5

2 of 15 is 3 so must be 6.

5

2

5

1

5

2

6

Now try these questions on your own.

Click again when you have worked out all the answers.

Need some more practise? Try Teacher Tools Fractions, Decimals and Percentages Book Numeracy resources

2) A car company can make 18 cars in 4 days. How many cars can they make in 3 days?

1) A newspaper company can print 84 newspaper in 12 minutes. How many newspapers can it print in 8 minutes?

Solve the following problems.

56

18