Ratios and Scale drawings

A ratio is a comparison of one thing with another.  It shows the relative size of two or more quantities. The order of the ratio is very important. a:b is not equal to b:a. Now let us find how to do ratios? A ratio can be expresses in three different ways:-

1. Fractional notation : 2/5
2. Odds notation: 2:5
3. Using the word “to” : 2 to 5

How to find ratios? Ratios can be solved by reducing them.  We can multiply or divide both the terms of ratio by the same number; it makes no change to the ratio. So this clearly answers how to solve ratios?

For example: - In a class of 20 students, 5 are girls and 15 are boys. What is the ratio of girls to boys?
Solution: - There are 5 girls and 15 boys.
The ratio of girls to boys will be 5:15
We can reduce this fraction by dividing both the terms by number 5
The ratio will be 1:3
Let us learn about ratio word problems now. Ratio word problems are problems that require use of ratios to relate the different quantities.
Following points should be kept in mind while solving ratio word problems:-

• Convert all the quantities to same units if required
• Write the quantities in the ratio as a fraction
• Remember to keep same quantities in numerator and denominator

Example:- There are blue and red ball in a bag, the ratio of blue balls to red balls is 5:6. If the bag contains 60 red balls, how many blue balls are there?
Solution: -
Let x be blue balls
Red/Green = 5/6 = x/60
X = 50 balls.
Let us learn about scale drawings. If any ratio is expressed in 1:n  form, then n is called the scale factor. It is not possible to draw on paper the exact size of real- life objects. Therefore we make use of scale drawing to draw such figures like a car, a building or any map.

Example: -A figure has a scale of 1:10 that means anything drawn with the size of “1” would have a size of “10” in real world.