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Define Numeric Ratio

Define numeric ratio:

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.

Example:

For every Spoon of sugar, you need 2 spoons of flour (1:2)

Source: Wikipedia


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Define numeric ratio:

The numeric ratio of two numbers p and q(q≠0) is the quotient of the numbers. The numbers p and q referred to as the conditions of the numeric ratio.

Types of ratios:

  1. Compounded ratios

  2. Duplicate ratios

  3. Triplicate ratios

Define compounded ratios:  

General format for compounded numeric ratio is

`p/q` *`r/s`=`(pr)/(qt)` 

 

 Example for compounded numeric ratios:

Example 1:

How to calculate ratios: `2/1`*`2/3`=`(2*2)/(1*3)`  or `4/3`or 4:3

Example 2:

How to calculate ratios: `6/1`*`2/3`=`(6*2)/(1*3)` or `12/3` or 12:3 or 4:1

Practice problem:

  1. How to calculate ratios:  `5/1`*`3/2`   Answer: `(5*3)/(1*2)` or `15/2` or 15:2

  2. How to calculate ratios: `3/2`*`3/2` Answer: `(3*3)/(2*2)` or `9/4` or 9:4 

Define duplicate numeric ratios:

 General format for duplicate ratio is

`(p/q)*(p/q)`=`(p^2)/(q^2)` 

Example for duplicate numeric ratios:

How to calculate numeric ratios: `3/2`*`3/2`=`(3*3)/(2*2)` or `(3^2)/(2^2)`  or `3^2`:`2^2`

Practice problem:

How to calculate numeric ratios: `(5/2)*(5/2)`   answer: `(5^2)/(2^2)` or `5^2`:`2^2`

Define triplicate numeric ratios:

General format for triplicates ratio is

`p/q``p/q``p/q`=`(p^3)/(q^3)`

Example for triplicate numeric ratios:

How to calculate numeric ratios: `7/2` * `7/2` * `7/2`=`(7*7*7)/(2*2*2)`=`(7^3)/(2^3)` or `7^3`:`2^3`

Practice problem:

How to calculate numeric ratios: `3/2` * `3/2` *`3/2`   answer: `(3^3)/(2^3)` or `3^3`:`2^3`


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More about numeric ratios:

Define Inverse numeric ratios:

It is often wanted to estimate the numbers of a numeric ratio in the inverse order. To do this, we simply exchange the numerator and the denominator. Thus, the inverse of 5:10 is 10:5. When the terms of a ratio are exchange, the INVERSE NUMERIC RATIO results.

For example, in problems 1 through 5, write the ratio as a fraction anddecrease to lowest terms. In problems 1 through 5, write the inverse ofthe given ratio.

Example problem for inverse ratios:

Example 1:

How to calculate inverse numeric ratios:  `15/50` 

Solution:

=`15/50`    (numerator and denominator are separated by 5)

=`3/10`    

Answer is `3/10` or 3:10

Example 2:

Solve `(10/5)*(2/3)` 

Solution:

=`(10/15)*(2/3)` 

= `20/45` (numerator and denominator are separated by 5)

=`4/9` 

Answer is `4/9`  or 4:9