Unit 2: Section 1 - Standard Form With Negative Indices Examples And Worksheets Page 5
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14Example 12
Divide £1170 in the ratio of 2 : 3 : 4.
(Add the ratios together: 2 1 3 1 4 5 9.)
_
2
Then the first part 5
of £1170 5 £260.
9
_
3
The second part
of £1170 5 £390.
5
9
_
4
The third part
of £1170 5 £520. (Check: £260 1 £390 1 £520 5 £1170.)
5
9
Exercise XX*
1 Divide $120 in the ratio 3 : 5.
2 Divide $350 in the ratio 1 : 6.
3 The fuel for a lawn mower is a mixture of 8 parts petrol to one part oil. How much oil is
required to make 1 litre of fuel?
4 A chicken stock contains chicken bones and chicken pieces in the ratio 20 : 7.
What weight of chicken pieces is needed to make 2 kg of stock?
5 Divide 702 in the ratio 1 : 2 : 3.
6 Divide 576 tonnes in the ratio 4 : 3 : 2.
7 Mr Chan has three daughters, An, Lien and Tao, aged 7, 8 and 10 years respectively.
He shares $100 between them in the ratio of their ages. How much does Lien receive?
8 A breakfast cereal contains the vitamins thiamin, riboflavin and niacin in the ratio
2 : 3 : 25. A bowl of cereal contains 10 mg of these vitamins. Calculate the amount of
riboflavin in a bowl of cereal.
Positive integer powers of numbers
Powers are used to write certain numbers in a convenient way. To help you understand how the
rules of indices work, study the table carefully.
Operation
Example
Rule
Multiplying
4
2
Add the indices
3
3 3
5 (3 3 3 3 3 3 3) 3 (3 3 3)
m
n
m 1 n
6
4 1 2
(a
3 a
5 a
)
5 3
5 3
5 729
Dividing
Subtract the indices
3 3 3 3 3 3 3
_____________
3
4
4 3
2
5 3
2
5 3
4 2 2
5 9
5
3 3 3
(a
m
4 a
n
5 a
m 2 n
)
Raising to a power
Multiply the indices
(3
4
)
2
5 (3 3 3 3 3 3 3) 3 (3 3 3 3 3 3 3)
(a
m
)
n
5 a
mn
5 3
8
5 3
4 3 2
5 6561
Example 13
Write 30
5
in standard form
30
5
5 (3 3 10)
5
5 3
5
3 10
5
5 243 3 10
5
5 2.43 3 10
7
5
Write 4
as a power of 2
4
5
5 (2
2
)
5
5 2
10
14
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