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## Ratio and Proportions Math trick Problem and solution

**Ratio:**

A ratio is a fraction that compares two quantities that are measured in the same units.

Ratio of two quantities a and b of the same kind is a/b is denoted by the a:b, and read as a is to b.

**Properties of the ratios:**

- The value of ratio never changed or we can say it is remains unchanged, if each of its terms are multiplied or divided by a same non-zero number.
- For a>b, if the same positive number is added to each term, the ratio decreases.
- For a<b, if the same positive number is added to each term, the ratio increases.

**Check Also: Exam Jagat**

**Part-to-Part Ratios:**

The ratio that compares one part to another part is called part-to-part ratio, denoted by part:part.

Example: If a bag contains marbles of colors red and blue with quantities 3 & 5 respectively, then ratio of the red marbles is known as part:part ratio

This would be denoted as;

Red marbles: Blue marbles

=3:5

**Part-to-Whole Ratios:**

If a set of objects is divided into two groups, in the ratio a:b, then the first group contains a/(a+b) objects and the second group contains b/(a+b) objects. This ratio is called part-to-whole ratio denoted as part:whole. Hence, the objects a and b would be a:(a+b) and b:(a+b) ratios with respect to the total objects.

**Example:** From recent example, the part-to-whole ratios can be shown as;

For red marbles= 3:8

For blue marbles= 5:8

**Note:**

- Ratio is the relation existing between any two quantities of the same kind.
- Order of the terms in the ratio is important. in the general for a is not equal b, the ratio a:b and b:a are different.
- Ratio of two quantities is an absolute number if it has no unit.

In a partnership if the investment are in the ratio a:b and the periods are in the ratio m:n, then they share the profits in the ratio am:bn.

**How to Determine a Ratio:**

Ratio represent how one number is related to another number.

A ratio may be written as A:B or A/B or by the phrase “A to B” .

A ratio of 1:5 says that the second number is five times as large as the first.

The following steps will allow a ratio to be determination if two numbers are known.

**Example :**

Determine the ratio of 24 to 40.

Divided both terms of the ratio by the greatest common factor ( 24/8=3, 40/8=5)

The ratio of 24 to 40 is 3:5

- Ratio is another name of the fraction. An equation in which two ratio are equal is called a proportions.
- Ratio is a quotient of one number a to another number b. It can be expressed in three ways.

- a:b
- a/b
- a÷b

The ratio a:b is read as a to b.

**Example**: Find the ratio of x to y from the equation 3x²+y²=4xy

**Solution: ** x²-4xy+y²=0

**Example:**If 4 boys can paint a fence in 5 hours. how many hours would it take 3 boys to paint the same fence?

**Solution**. This problem involves the concepts of inverse relationship.