Brmmm! Brmmm!

I am learning to solve problems in which a fraction measures another fraction.

A ferry has a full tank of petrol. Every time the ferry crosses the harbour it use up three eighths of a tank. How many trips can the ferry make before it needs to fill up?

1 full tank of gas.

We can record this as 1 ÷ = ?8

3

One full tank Amount of petrol used on each tripShared between

Eighths

= 1 trip8

3

= 2 trips8

6

You can see we have only have enough petrol left for two thirds of a crossing.

So 1 ÷ = 2 8

33

2trips

3

22 is the same as

3

8Do you see any pattern?

A bus has a full tank of petrol. The bus uses two sevenths of its tank on every complete loop. How many loops can it make before it must fill up?

1 full tank of gas.

We can record this as 1 ÷ = ?7

2

One full tank Amount of petrol used on each tripShared between

sevenths

= 1 trip7

2

= 2 trips7

4

You can see we have only have enough petrol left for half the loop.

So 1 ÷ = 3 7

22

1trips

2

13 is the same as

2

7

Notice the pattern again?

= 3 trips7

6

is the reciprocal of2

7

7

2

A shuttle bus has three quarters of a tank of petrol. It takes one sixth of a tank to make one round trip. How many trips can it make before it must refuel?

We can record this as ÷ = ?6

1

Amount of tank that is full. Amount of petrol used on each tripShared between

4

3

3 quarters (how much fuel we have)Sixths (we use one sixth on every round trip)

Let’s covert them both into twelfths so they have the same denominator.

You can see = 4

3

12

9

You can see = 6

1

12

2

12

9

12

2÷ = ? (How many measured )

12

212

9

12

9

12

2÷ = 4 wholes and one half

2

14

Let’s use the answers we have already calculated and see if we can spot a pattern.

÷ = 8

3

3

81

13

8

3

81

1 X =

7

22

7

1

1 ÷ =

2

72

7

1

1 X =

4

3

12

2÷ =

2

9

4

3

2

12X =

8

36

2

9=

Change to multiplication

8 thirds is the reciprocal of 3 eighths

Change to multiplication

7 halves is the reciprocal of 2 sevenths

Change to multiplication

12 halves is the reciprocal of 2 halves

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

8

6

5

2÷ =

12

7÷ = 2)

1) 5

22

1÷ =

6

5

3

1÷ =6)

5)

Solve the following problems.

8

15

12

21

5

4

6

15

3

1

=

= =

16

30

4

72

5