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# Ratio and Proportion

Maths | 10-12 yrs | Interactive

## What is a ratio?

Ratio is a relationship between two numerical values. It shows how many times one value contains another value.

### Examples of ratio

When we make mango crush, we are told to add one part crush to four parts water. Which means if I take one cup of crush, I need to add four cups of water. This is a relation that can be written as 1:4.

## How to solve ratios?

Sam wants to make tea with the ratio of milk to water to be 2 : 3. If he needs to make 5 cups of tea, how much milk and water will Sam need?

Answer – Sam needs a ratio of 2 : 3, thus the total parts of his mixture are 2 + 3 = 5. Since he is making 5 cups of tea, 1 cup can be said to be equal to one part.

Milk has to be 2 parts out of 5 so Sam will need 2 cups of milk.
Water has to be 3 parts out of 5 so Sam will need 3 cups of water.

## What is a proportion?

Proportion is used to describe how much of a certain component is there in something. Like our mango crush will always be one part of crush and four parts of water. Thus there is a total of 5 parts in our crush. So mango crush will always be one part out of five and thus ⅕.

## Types of proportion

### 1. Direct proportion

In the case of our crush, if we take one cup crush, we need to add four cups water. If we take two cups of crush, we will have to add eight cups of water. Thus if the quantity of one proportion increases, the quantity of the other also increases. This is called Direct Proportion.

### 2. Indirect proportion

If the quantity of one value increases, the other goes down, and vice-versa. This relationship is called Indirect Proportion.

### Examples of proportion

In some cases like in a race, the relation between speed and time taken to cover a specific distance is proportional but not directly.

If we are travelling at 20 km per hour, we will cover 20 kilometer in one hour.
If we are travelling at 40 km per hour, we will cover 20 kilometer in half an hour.

As you can see, if the quantity of one value increases, the other goes down.

## Proportion formula

If a:b::c:d then a/b=c/d

## How to solve a proportion

If a car travels 30 km in one hour, then how far will it travel in two hours?
Answer – Let us assume the car travels Z km in two hours.

By the formula of proportion-
30km : 1 hour = Z km : 2 hours

So 30/1= Z/2

Z= 30/1 x 2

Z = 60

Thus the car will travel 60 km in two hours.

1) Rachel needs to make lemonade from the lemonade syrup, she has to add syrup to water in the ratio of 1:6. How will Rachel make 14 cups of lemonade?

Options
A) 12 cups water to 2 cups syrup
B) 6 cups water to one cup syrup
C) 4 cups water to 10 cups syrup
D) 2 cups water to 12 cups syrup

2) Emma is told to make mix fruit juice with a 1:1 ratio of orange juice to pineapple juice. To make 1 liter of juice how much orange juice will she need

Options
A) 1.5 liter of orange juice
B) 1 liter of orange juice
C) 0.5 liter of orange juice
D) 0.3 liter of orange juice

1) If a car goes 20 km in two hours, how far will it go in one hour?

Options
A) 40 km
B) 30 km
C) 10 km
D) 5 km

2) Casper walks 5 km in one hour. The shop is half an hour away, how far is the shop in terms of km?

Options
A) 2.5 km
B) 3 km
C) 1 km
D) 4 km

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