Number
Fractions
of the bar of chocolate is shaded.
of the bar of chocolate is shaded.
* of the bar of chocolate is shaded. (* read this as two-quarters)
Can you see that is the same as ?
You can produce equivalent fractions like this by multiplying both the top and the bottom of the fraction by the same number.
× =
× =
× =
× =
Now try these
Exercise 1
1. × =
2. × =
3. × =
4. × =
5. × =
Exercise 2
You know that is the same as (top and bottom both multiplied by 2)
1. Now try these:
a) =
b) =
c) =
d) =
e) =
f) =
Before you can compare fractions the bottom number (denominator) must be the same.
e.g. Which is smaller?
or
This becomes
or (because is eqivalent to )
is smaller than
therefore is smaller.
2. Which is smaller?
a) or
b) or
c) or
4. Put the following fractions in order beginning with the smallest
a)
b)
c)
A mixed number / fraction is a whole number and a fraction e.g. 1
As 1 = this mixed number can be written as i.e. +
This is called an improper fraction.
5. Try to make these mixed numbers into improper fractions:
a) 1 b) 1 c) 1
d) 1 e) 1 f) 1
6. Now convert these improper fractions to mixed numbers:
a) b) c)
d) e) f)
Lets look at
Remember, the number at the bottom tells you how many parts there should be in
the whole number.
In there are 2 whole numbers and three parts left over i.e.
= 2
7. Try these
Improper fraction / Mixed number/ e.g. 2
e.g. / 3
2
2
5
Before you can compare mixed fractions and improper fractions you must convert them to the same type of fraction.
e.g. 1
becomes
You then convert these fractions to equivalent fractions with the same denominator [number at the bottom].
e.g.
Largest to the smallest is
1
8. Put the following in order beginning with the largest
a) 1
b) 1 1
c) 2 2
d) 2 1
e) 1 1
f)
Exercise 3
1. What would you divide by to get
a) b) c)
Let’s find fractions of numbers, e.g., of 90 = 45 because = 45.
2. of a) 24 b) 36 c) 75 d) 113 e) £92 f) £15
3. of a) 8 b) 48 c) 25 d) 69 e) £24 f) £26
4. of a) 18 b) 33 c) 96 d) 10 e) £9 f) £924
In the next few questions you are asked to describe numbers as ‘ ’, ‘more than ’ or ‘less than ’. Start by working out what of the number is, then you can judge if the number you are given is less than that, or more than that. Circle the correct answer.
(more than) (less than)
5. 50 is of 100
6. 62 is of 92
7. 11 is of 23
8. 3.5 is of 6
9. 6.5 is of 13
10. 1000 is of 1362
Check your answers. Are you happy about finding ?
Now let’s look at .
To find of 56:
of 56 is 28
of 28 is 14 so = 14
If you want to see if a number is nearest to, , , you need to work in stages.
e.g. What fraction is 26 of 104?
a) Find of 104, which is 52
b) Find of 104, which is 26 so 26 is of 104
Try these:-
11. What fraction is 13 of 26?
12. What fraction is 15 of 60?
13. What fraction is 90 of 360?
14. What fraction is 6 of 12?
15. What fraction is 9 of 18?
16. What fraction is 2.5 of 5?
17. What fraction is 1.25 of 5?
18. What fraction is 500 of 2000?
19. What fraction is 50 of 200?
20. What fraction is 10 of 20?
Now let’s look at .
If the number is quite a bit more than , then you can describe it as ‘about ’.
To give a number that is ‘about ’ of 40, remember that 20 is , 10 is ,
so any number around 30 is about (20 + 10 = 30).
21. If 17 is of 34, and 8.5 is a , what is about of 34?
22. Give a number that is about of 13. (is 6.5, is 3.25)
23. Give a number that is about of 20
In a fraction the bottom number is the denominator. This is the number that you divide by to find one part
e.g to find , divide by 5.
In a fraction the top number is the numerator.
This shows how many parts.
e.g to find , divide by 5, muliply by 2
of 20 = x 2 = 8
to find , divide by 5, mulitply by 4
of 30 = x 4 = 24
24. What is of 15?
25. What is of 15?
26. What is of 50?
27. What is of 50?
28. What is of 40?
29. What is of 40?
Workbook 5 Level 1 Numeracy/Application of Number Ó West Nottinghamshire College 2004
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