Ratio in simple words means comparison of pair of numbers. Ratio is nothing but one with respect to other. A ratio can be used to compare two numbers using a fraction. Ratios can be written in three different ways:
(1) 5 to 3
(2) 5:3
(3) $\frac{5}{3}$
They all have the same meaning. A class have 35 students, 20 students are boys and 15 are girls. I can compare number of boys to girls using the ratio `(20)/(15)` (or 20:15; or 20 to 15). You can reduce this fraction to `(4)/(3)` by dividing both numerator and denominator by 5.that is for every four boys there are 3 girls.
Notation and terminology of ratios:
The ratio of quantity A and B can be expressed as
• The ratio of A to B
• A is to B
• A: B
The quantity A and B are also termed as antecedent and consequent respectively.
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The numeric ratio of two numbers r and s(s?0) is the part of the numbers. The numbers r and s are called as the conditions of the numeric ratio.
Types of ratio- computing for ratio:
Compounded ratio
Duplicate ratio
Triplicate ratio
Standard format for compounded numeric ratio is
$\frac{A}{B}$ x $\frac{C}{D}$ = $\frac{AC}{BD}$
Example : Compute for compounded ratio of `5/4` and `3/2`
Solution: `5/4` X `3/2`
= `15/8` is 15:8
Duplicate ratio:
Regular format for duplicate ratio is
$(\frac{A}{B})$ x $(\frac{A}{B})$ = $\frac{A^2}{B^2}$
Example : Computing for duplicate ratio:of `5/3`
Solution: `5/3`X `5/3`
= `5^(2)/3^(2)`
= `25/9` or 25:9
Triplicate ratio:
Regular format for triplicates ratio is
$(\frac{A}{B})$ x $(\frac{A}{B})$ x $(\frac{A}{B})$ = $\frac{A^3}{B^3}$
Example:compute the triplicate ratio of `5/3`
Solution: `5/3` X `5/3` X `5/3`
= `5^(3)/3^(3)`
= `125/27` or 125 : 27
A ratio is can always be change in the from of $\frac{p}{q}$ , where q is not equal to zero. Then try to find largest number by which we can divide numerator and denomirator , and quotient is always in natural number.
Examples : A class have 10 boys and 8 girls, find the ratio of boys and girls ?
Solution: 10 boys to 8 girls
= $\frac{10}{8}$
= $\frac{5}{4}$ (here we divide numerator and denomirator by 2, and quotient is 5 and 4, which are natural numbers.)
A ratio is a fraction that is numerator and denominator can have different units. For example: if you travel 100 miles in 2 hours, we can write that as a ratio:
2hours
100miles
And we can simplify that ratio, using the same techniques for simplifying fractions:
2hours 100miles = 1hour 50miles
If there are 4 oranges and 5 apples, the ratio of oranges to apples is exposed as 2:3; where as the fraction of oranges to total fruit is `(4)/(5)`
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