# Ratio Calculators

## Knowledge

### What is ratio in math?

#### •The definition of ratio:

A ratio says how much of one thing there is compared to another thing. When describing a ratio, the first number is known as the 'antecedent' and the second is the 'consequent'. So, in the ratio 5:1, the antecedent is 5 and the consequent is 1.

Ratio can be shown in different ways:

1. Use the ":" 5:1.

2. The ratio of A to B: 5 to 1.

3. A fraction with A as numerator and B as denominator that represents the quotient.

#### •The different types of ratios:

1. Compounded Ratio: The compounded ratio of the two ratios a : b and c : d is the ratio ac : bd, and that of a : b, c : d and e : f is the ratio ace : bdf

2. Duplicate Ratio: The duplicate ratio of the ratio a : b is the ratio a^{2}: b^{2}

3. Reciprocal Ratio: The reciprocal ratio of a:b is (1/a):(1/b), where a≠0 and b≠0

4. Ratio of equalities: If the antecedent and consequent are equal then the ratio is called ratio of equality, like 6:6.

5. Ratio of Inequalities: If the antecedent and consequent are not equal then the ratio is called the ratio of inequality, like 4:7.

### Proportion vs. Ratio

•Proportion:The proportion is usually 100% as the proportional coefficient, which is used to describe the proportion or distribution of each component in the whole, such as what accounts for a large proportion of what. It emphasizes the relationship between one thing and other things in terms of quantity, size, etc.

•Ratio:A ratio is a comparison of two numerical values; it is a portion of a number. A ratio may also be expressed as a fraction or a division problem. It emphasizes the ratio of whole to part and part to part.

### How to find the ratio?

Ratios can describe quantity, measurements or scale. Usually, there are three steps to find the ratio:

•Simplify ratios or create an equivalent ratio when one side of the ratio is empty.

•Solve ratios for the one missing value when comparing ratios or proportions.

•Compare ratios and evaluate as true or false to answer whether ratios or fractions are equivalent.

Now, let’s see some examples of finding ratio.

## Example 1:

Find the x value of the ratio 10 : x = 12 : 16

Solution:

*10*

*x*=

*12*

*16*➡

*5*

*x*=

*6*

*8*

*5×8*

*6*=

*40*

*6*=

*20*

*3*

## Example 2:

In a gym class, 15 students are playing baseball, 11 students are playing basketball, and 4 students are playing football. What is the ratio of the number of students playing football to the number of baseball in this class?

Solution: This problem gives us all the information we need to express the ratio:

4 students are playing football : 15 students are playing baseball = 4 : 15

## Example 3:

Andrew and James have 400 sweets and they need to share them in the ratio 5:3. How many sweets does each of them receive?

Solution: