Fractions As Ratios Worksheet Page 4
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1
2
3
4nuMber AnD AlgebrA
• real numbers
WorkeD exAMple 28
Share the amount $500 000 in the ratio 3 : 7.
Think
WriTe
Total number of parts = 3 + 7
Calculate the total number of parts in the ratio.
1
= 10
3
First share =
ì $500 000
The fi rst share represents 3 parts out of a total of 10,
The fi rst share represents 3 parts out of a total of 10,
The fi rst share represents 3 parts out of a total of 10,
2
10
3
3
so fi nd
of the total amount.
= $150 000
10
7
Second share =
ì $500 000
The second share represents 7 parts out of a total of 10,
The second share represents 7 parts out of a total of 10,
The second share represents 7 parts out of a total of 10,
3
10
7
7
so fi nd
of the total amount.
= $350 000
10
We can mentally check our answer by adding the two shares together. The total should be the
■
same as the amount that was originally divided.
WorkeD exAMple 29
Concrete mixture for a footpath was made up of 1 part of cement, 2 parts of sand and 4 parts of
2
blue metal. How much sand was used to make 4.2 m
of concrete?
Think
WriTe
Total number of parts = 1 + 2 + 4
Find the total number of parts.
1
= 7
2
There are 2 parts of sand to be used in the mixture,
Amount of sand =
ì 4.2 m
2
2
7
2
so fi nd
of the total amount of concrete made.
= 1.2 m
2
7
reMeMber
1. Ratios compare quantities of the same kind.
2. The ratios themselves do not have a name or unit of measurement.
3. The order of the numbers in a ratio is important.
4. Before ratios are written, the numbers must be expressed in the same units of
measurement.
5. Ratios contain only whole numbers.
6. If each number in a ratio is multiplied, or divided by the same number, the equivalent
(or equal) ratio is formed.
7. It is customary to write ratios in the simplest form. This is achieved by dividing each
number in the ratio by the highest common factor (HCF).
8. To form a ratio, using fractions, convert the fractions so that they have a common
denominator and then write the ratio of the numerators.
9. To share a certain amount in a given ratio, fi nd the total number of shares (parts) fi rst.
The size of each share is given by the fraction this share represents out of the total
number of shares.
118
Maths Quest 7 for the Australian Curriculum
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