Page 4 - 6-Math-6 RATIO AND PROPORTION
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Therefore, we can simplify a ratio, as well as, a common fraction, by
dividing them by their HCF. For instance, consider the students of a
class, in which 25 are girls and 30 are boys. To find the ratio of girls is
to boys, we can write it as.
Girls Boys
25 : 30
( To reduce it, divide by their HCF.)
Girls Boys
25'5 : 30 ' 5
5 6
In this example, we can observe that the ratio 5 : 6 has no common
factor and both elements are natural numbers. This is called the
reduced form or the lowest form of a ratio. When the two elements
of a ratio are fractions, then first multiply them by the LCM of their
denominators to change them into the integers. For example,
version: 1.1 • Equivalent Ratios
We know that a ratio is another form of a common fraction. Therefore,
the same rule for finding the equivalent fractions can be used to get
equivalent ratios.
Rule: When both the elements of a ratio are multiplied or divided
by same number, the value of a ratio is not changed. For example,
suppose we want to find some equivalent ratios of any ratio 1:2. We
can do it as:
1:2, 1x2:2x2 = 2:4, 1x3:2x3 = 3:6, 1x4:2x4 = 4:8 and so on.
1:2 = 2:4 = 3:6 = 4:8 = ...
Similarly , We can prove that 4:8 = 3:6 = 2:4 = 1:2
• Relationship between ratio and fraction
Actually, ratio is the simplest form of a common fraction, in which
the numerator denotes antecedent and the denominator denotes
consequent.
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