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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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Ratio Definition

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The ratio of two numbers u and v (v $\neq$ 0) is the section of the numbers. The numbers u and v are called as the terms of the ratio.

What is Ratio

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The learning ratio is a comparison by division method. We compare the two quantities in terms of ‘how many times’. This comparison is known as the Ratio. We denote ratio - using symbol ‘ : ’

Different Types of Ratios

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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:

  1. Compounded ratio

  2. Duplicate ratio

  3. Triplicate ratio

Compounded 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

How to Solve a Ratio

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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.)

Finding Ratios

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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:


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)`

Solved Examples

Question 1: In a bag of red and green balls, the ratios of red ball to green ball are 3:4. If the bag contains 120 green balls, how many red balls are there?
 Step 1: Assign variables:

Let x = red sweets

Write down the items in the ratio as a fraction.

`(Red)/(Green)` =`(4)/(5)` = `(x)/(120)`

Step 2: Solve the equation

Cross multiply the equation

4 × 120 = 5 × x
480 = 5x

Isolate variable x

X  = `(480)/(5)` = 96

Answer: There are 96 red balls.

Question 2: A special mixture contains rice and corn in the ratio of 2:6. If a bag contains 3 pounds of rice, how much corn it contains?
Step 1: Assign variables:

Let x = amount of corn

Write down the items in the ratio as a fraction.

`(Rice)/(corn)` = `(2)/(6)` =`(3)/(x)`

Step 2: Solve the equation

Cross multiply the equitation

2 × x = 3 × 6
2x = 16

Isolate variable x

X = `(18)/(2)` = 9

Answer: The bag contains mixture 9 pounds of corn.

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