Unit 2: Section 1 - Standard Form With Negative Indices Examples And Worksheets Page 3

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d The volume of a cup of tea is 200 cm
3
.
How many molecules of water would the cup hold?
If all these were placed end to end in a straight line, how long would the line be?
Take the circumference of the Earth to be 40 000 km.
How many times would the line of molecules go around the Earth?
Four rules of fractions
This section will give you practice in using fractions. The questions will help you to understand
much of the algebra in this unit.
Addition and subtraction
A common denominator is required.
Example 3
Example 4
Example 5
Addition
Subtraction
With mixed fractions
3
_
_
3
_
_
_
3
_
1
2
1
3
2 1
1
2
4
6
4
5
3
4
__
__
____
__
__
__
_____
__
__
_
9
2
9 1 2
11
15
8
15 2 8
7
10
7
5
1
5
5
5
2
5
5
5
2
12
12
12
12
20
20
20
20
3
4
______
40 2 21
5
12
19
__
5
12
__
7
5 1
12
Multiplication and division
Convert mixed fractions into improper fractions.
Example 6
Example 7
Multiplication
Cancelling
3
_
3
_
5
_
1
_
1
1
3 2
3
9
7
4
5
_
_
____
__
__
__
__
______
7
3
7 3 3
21
1
14
15
14 3 15
5 1
5
3
5
5
5
3
5
4
5
4 3 5
20
20
9
7
9 3 7
Divide top and bottom by 7, and by 3.
____
__
_
2 3 5
10
1
5 3
5
5
3 3 1
3
3
Example 8
Example 9
Division
Multiplying with a whole number.
3
_
__
5
3
_
÷
3 7
4
11
4
Turn the divisor upside down and multiply.
Change the whole number into a fraction.
_
__
_____
__
__
_
_
____
__
_
3
11
3 3 11
33
13
3
7
3 3 7
21
1
5 1
5 5
5
3
5
5
5
3
5
5
4
5
4 3 5
20
20
4
1
4 3 1
4
4
Example 10
Dividing into a whole number.
1
_
8 ÷ 1
2
_
_
_
_
____
__
_
8
3
8
2
8 3 2
16
1
÷
5 5
5
5
3
5
5
1
2
1
3
1 3 3
3
3
12

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