Feeding Pets

I am learning to find fractions between two other fractions.

3

1

4

30 1

12

7

And many more.

e.g.

Sue likes chocolate. of a bar is never enough but always

makes her sick. What fraction of a bar could she have?

3

12

1

One whole bar.One third (not enough)

One half (too much)

Between here and here is the perfect amount.

Let’s start by converting the fractions to decimals and see if that helps.

3

1= 0.33

2

1= 0.5

Now we can just choose any decimal between 0.33 and 0.5

I’m going to choose one that I can easily turn back into a fraction.

0.4 =10

4or

5

2

You can see that this is one answer but there is actually an infinite number that fit between these fractions.

Craig also likes chocolate. of a bar is never enough but always

makes him sick. What fraction of a bar could he have?

5

1

3

1

One whole bar.

One fifth (not enough)One third (too much)

Between here and here is the perfect amount.

Let’s start by converting the fractions into equivalent fractions with the same denominator.

The lowest common multiple of 5 and 3 is 15.

5

1

15

3X3X3 3

1

15

5X5X5

Now its easy to choose a fraction between and . 15

3

15

5

I’m going to chose 15

4

You can see that we can solve these types of problems by either turning the fractions into decimals or changing the fractions so they have a common denominator.

Find a fraction between and 10

2

20

8

Solve using decimals. Solve using equivalent fractions.

10

2= 0.2

20

8= 0.4

Choose a decimal between 0.2 and 0.4

0.3 =10

3

There are of course an infinite number of possible solutions.

10

2=

20

8

20

4

Choose a fraction between and 20

4

I’m going to choose20

6

Which is equivalent to10

3

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

4

1

8

4and

10

8

50

38and 2)

1) 4

33

1and

3

112

8and6)

5)

Find a fraction between the fractions below. Only one possible answer will be shown below. There are of course an infinite number of possible answers.

Possible solution =

Possible solution =

Possible solution =

Possible solution =

8

3

100

77

10

7

12

5