Unit 10 Section 1 : Fractions

This unit deals with fractions. Fractions are numbers of the form where a and b are whole numbers and b is not zero.

This section looks at the meaning of fractions when related to shapes.

Example Question

Look at the shapes below which have been drawn on squared paper.
Example 1
The shape in part (a) is divided into 4 triangles. Each triangle is one quarter () of the whole shape.

Three of the triangles are shaded, so we say that the fraction which is shaded is .

Example 2
The shape in part (b) is divided into 8 rectangles, three of which are shaded.

We say that of the shape is shaded.

Practice Questions
Work out the answer to the two questions below then click on the button marked Click on this button below to see the correct answer to see the answers.
What fraction of the shape in part (c) is shaded?

What fraction of the shape in part (d) is shaded?

Note that the fraction in part (d) can also be written as or .

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

In some of the questions below, you are asked to shade in sections of a diagram. Click with the left mouse button to shade in a section, and if you want the section to go back to being unshaded, click again with the left button. When you are satisfied that you have shaded the correct regions, click on the 'check' button to see if you have answered correctly.

Question 1
Work out what fraction of each of the shapes below has been shaded.
Each answer has two boxes. Put the numerator in the top box and the denominator in the bottom box, for example:
(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Question 2
Shade the given fraction in each of the rectangles below.
(a)
1
3
(b)
3
5
(c)
7
9
(d)
3
4
(e)
5
8
(f)
3
10

Question 3
Look at the rectangle below.
(a) How many squares are there in total in the rectangle?

(b) If the rectangle was divided into exactly 8 equal parts, how many squares would be in each part?

(c) Shade in one eighth () of the rectangle.

(d) What fraction of the rectangle has not been shaded?

Question 4
Shade the given fraction in each of the rectangles below.
(a)
1
4
(b)
4
5
(c)
7
8
(d)
2
3
(e)
7
16
(f)
9
12
(g)
7
10
(h)
13
20

Question 5
Shade the given fraction in each of the rectangles below.
(a)
1
2
(b)
1
4
(c)
1
3
(d)
1
6
(e)
1
12

Question 6
Below is a rectangle which you can shade by clicking on sections with the left button.

(a) Shade of the rectangle.

(b) Now shade another of the rectangle.

(c) What is the total fraction now shaded?

(d) What fraction is left unshaded?

Question 7
Sarah shades of a shape.

What fraction of the shape is left unshaded?

Question 8
A cake is divided into 12 equal parts. John eats of the cake and Kate eats another of the cake.

What fraction of the cake is left?

Question 9
A car park contains 20 spaces. There are 17 cars parked in the car park.

(a) What fraction of the car park is full?

(b) What fraction of the car park is empty?

Question 10
Ali eats of the sweets in a packet. Tariq eats another of the sweets.

(a) What fraction of the sweets has been eaten?

(b) What fraction of the sweets is left?


You have now completed Unit 10 Section 1
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Produced by A.J.Reynolds January 2001