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UNIVERSITY OF DUNDEE
SCHOOL OF NURSING AND MIDWIFERY
Numeracy help sheet number 1
Fractions
A fraction is a part of a whole. For example ½ (a half) or ¼ (a quarter)
The bottom number, the denominator, tells us how many equal parts the whole has been split into.
The top number, the numerator, tells us how many of these parts we have.
Things that you should be able to do with fractions:



Simplify them
Multiply them
Divide them
You can simplify a fraction if you can divide the top part and the bottom part by the same number.
The most common are to divide by 2, 3, 5 or 10.
Examples:
Original
2
4
12
15
25
100
200
1000
Simplified
1
2
you can divide the top and bottom by 3, giving 4
5
you can divide the top and bottom by 5, giving 5
20
you can divide the top and bottom by 10, giving 20
100
Hint – can you do any more to the last 2?
you can divide the top and bottom by 2, giving
Simplify (and there may be more than one step to get it as simple as possible):
Original
2
8
10
15
250
1000
30
90
66
99
Simplified
you can divide the top and bottom by ___, giving
you can divide the top and bottom by ___, giving
you can divide the top and bottom by ___, giving
you can divide the top and bottom by ___, giving
you can divide the top and bottom by ___, giving
Multiplying Fractions
To multiply a fraction by a whole number, you just multiply the top by the number.
To multiply a fraction by another fraction, multiply the tops together, and the bottoms together, then
simplify
Examples
F1x
F 2 working
Giving
Can this be simplified?
1
3
x3
3
3
1
1
Or just 1
1
5
x2
4
1x2
5x4
2
20
1
10
5
9
x4
7
5x4
9x7
20
63
No more
Simplification
Try these
1
2
x3
1
4
x1
2
Dividing Fractions
To divide a fraction by another fraction, turn the second one over, and then multiply!
Examples
F1
÷
1
3
F2
÷1
4
Turn it
over
1
x4
3
1
1
2
÷2
3
1
2
5
9
÷4
7
5
9
Try these
1 ÷1
2
4
1
4
÷2
3
multiply
Giving
1x4
3x1
4
3
x3
2
1x3
2x2
3
4
x7
4
5x7
9x4
35
36
DECIMALS
Numbers like these are all decimals: 2.5, 3.6, 1.333, 10.5
The decimal point(.) is used the distinguish the parts of the number.
Numbers to the left of the decimal point are the normal counting numbers or whole numbers.
Numbers to the right of the decimal point are parts of the whole number.
If a number does not have a value for a column a 0 is used.
The
number
2.02
3.5
75.6
2050.004
Thousands Hundreds Tens Units Decimal Tenths Hundredths Thousandths
point
2
0
2
.
3
5
.
7
5
6
.
2
0
5
0
0
0
4
.
Now try some of these yourself
1345.76
3425
0
1
0
3
2
2
0
6
.
.
.
0
0
Rules and hints

To multiply by 10 the decimal point is moved one place to the right.

To multiply by 100 the decimal point is moved 2 places to the right.

To multiply by 1000 the decimal point is moved 3 places to the right.
Example 232.15 x 10
- move the decimal point to the right 1 place
- 2321.5

To divide by 10 the decimal point is moved one place to the left.
Example 94.1 ÷ 10
- move the decimal point to the left 1 place
- 9.41
Of interest: If dividing by a number less than 1, the answer will be larger than what you started
with!
Try these multiplications and divisions:
345.23 x 10
16 x 100
654.12 ÷ 10
654.12 ÷ 100
0
Conversions
The metric system always uses the rule of 1000 between different units, so if you know how to
multiply or divide by 1000, then just use the same principles
1000 micrograms = 1 milligram
1000 milligrams = 1 gram
1000grams
= 1 kilogram
Examples:
Convert 1456 micrograms to milligrams
This is a division problem because micrograms are smaller than milligrams
So divide by 1000
1456 ÷ 1000 - move decimal point 3 places to the left
= 1.456
Convert 250 kilograms to grams
This is a multiplication problem because kilograms are bigger than grams
So multiply by 1000
250 x 1000 - move decimal point 3 places to the right
= 250 000
Try these:
Convert 25 grams to milligrams
Convert 300 milligrams to grams (hint: you always need something in front of the decimal point)
Convert 155 grams to micrograms (hint: you might find it easier to do it in 2 stages – grams to
milligrams, then milligrams to micrograms)