RATIO AND PROPORTION

RATIO

A ratio compares things. The things may be numbers, masses, amounts of money,etc. For example:if we have five boys and seven girls in a class, then we say that the ratio of the boys to girls is 5 to 7. We write the ratio as 5:7. The colon(:) means 'to'.
A ratio a:b can also be written as a common fraction a/b. So 5:7 can be written as ⁵/₇. To compare two or more ratios, you can rewrite them as common fractions with common denominator.
For example, to compare 3:7 and 4:9,we write them as common fractions ³/₇and ⁴/₉ respectively. Then we write them with common denominator. Ie. ²⁷/₆₃ and ²⁸/₆₃".
Therefore 3:7 is smaller than 4:9
The order in which the ratio is given is important l. The 'thing' that is given first in the comparison must be written first in the ratio.
For example, the ratio of boys to girls is 5:7. Also the ratio of girls to boys is 7:5.
A ratio with a : sign has no units of measure. It just has numbers.
For example, the ratio of 4kg to 1kg is written as 4:1
Ratios may be simplified by dividing each part by the same number. In some problems the given ratio is not in its simplest form so change it to the simplest form first.
For example, 12:4 is the same as 3:1 and 9:6 is the same as 3:2.
Multiplying each part of the ratio by the same number also gives an equivalent ratio. Just like equivalent fractions.
For example, 2:3 is equivalent to 4:6" or 8:12 or 10:15

TO EXPRESS TWO QUANTITIES AS A RATIO

They must have the same units of measure. For example, 4kg:1kg not 4kg:40g. If they are not the same, then you must change them to the same unit.
For example, a ratio of 2kg: 50g is 2000g:50g

END OF LESSON EXERCISE 

Change the following ratios into its simplest form.
1. 25:5
2. 128:64
3. 10:4
4. 5:5
5. 72:36