What is Ratio and Proportion?

Ratio and proportion are mathematical concepts that help us make comparisons and solve problems in our daily lives. Whether we are dividing a pizza among friends or planning a trip, understanding ratios and proportions can be very useful. In this article, we will explain these concepts in simple terms and provide you with some examples to help you understand them better.

Ratio

Ratio is a way to compare two or more things that have something in common. For example, let's say we have 10 apples and 5 oranges. We can compare the number of apples to the number of oranges by using a ratio. A ratio is a way of showing the relationship between two numbers.

For example,

The ratio of apples to oranges is 10:5 or 2:1. This means that for every 2 apples, there is 1 orange.

Another example,

Of a ratio is if we have a pizza that is cut into 8 slices and 3 of the slices are pepperoni, the ratio of pepperoni slices to total slices is 3:8.

Ratios are very useful in many situations, such as cooking, construction, and finance.

Proportion

Proportion is an equation or statement that is used to depict that the two ratios or fractions are equivalent. Two equivalent ratios are always in proportion. Proportions refer to the equality of two ratios and are denoted by the symbol (: :). They help us to solve for unknown quantities.

There are two types of proportions.

• Direct Proportion
• Inverse Proportion

Direct Proportion

Direct proportion is a concept in math that helps us understand how things change when we increase or decrease one of them. It means that as one thing increases, the other thing also increases, and as one thing decreases, the other thing also decreases.

For example, let's say you are baking cookies and you need to use flour and sugar. If you increase the amount of flour, you will also need to increase the amount of sugar to keep the recipe balanced. This is because the amount of sugar needed is directly proportional to the amount of flour used.

Inverse Proportion

Inverse proportion is a concept in mathematics that shows how two values are related to each other. Inverse proportion means that as one value increases, the other value decreases. For example, imagine you are filling up a glass with water. If you increase the amount of water in the glass, the level of air in the glass decreases. This is because the amount of water and air are inversely proportional to each other.

Ratio and Proportion Formula

The formula for ratio is expressed as a : b ⇒ a/b, where,

• a = the first term or antecedent.
• b = the second term or consequent.

Now, in order to express a proportion for the two ratios, a : b and c : d, we write it as 

a:b::c:d ⟶ ab=cd�:�::�:�⟶��=��

• The two terms b and c are called mean terms.
• The two terms a and d are known as extreme terms.
• In a: b = c : d, the quantities a and b should be of the same kind with the same units, whereas, c and d may be separate of the same kind and of the same units.
• The proportion formula can be expressed as, a/b = c/d or a: b:: c : d.
• In proportion, the product of the means = the product of the extremes. Therefore, in the proportion formula a: b:: c : d, we get b × c = a × d.

Difference Between Ratio and Proportion

The difference between ratio and proportion can be seen in the following table.

Ratio	Proportion
A comparison of two or more quantities that have the same unit of measurement.	The equality of two ratios.
Can be written in different forms, such as 2:1 or 2/1.	Two ratios are proportional if they have the same value.
Represents how many times one quantity is greater than another.	When two ratios are proportional, it means that they have the same value.
Example: The ratio of boys to girls in a class is 2:3.	Example: If the ratio of boys to girls in a class is 2:3, and there are 10 boys, then there must be 15 girls for the ratios to be proportional.

Applications of Ratio and Proportion

Here are five possible applications of ratio and proportion that can be explained to 10-year-olds:

1. Cooking: When we cook, we use ratios and proportions to measure ingredients in the correct amounts. For example, a recipe may call for a ratio of 2 cups of flour to 1 cup of milk to make pancakes.
2. Scaling drawings: Architects and designers use ratios and proportions to scale their drawings and create blueprints. For example, a blueprint may have a scale of 1 inch to 1 foot, which means that 1 inch on the blueprint represents 1 foot in real life.
3. Finance: In finance, ratios and proportions are used to analyze financial statements and make investment decisions. For example, a company may use the ratio of its earnings to its revenue to measure its profitability.
4. Construction: Engineers and construction workers use ratios and proportions to calculate the measurements of buildings and structures. For example, the ratio of the height of a building to its width may be used to determine the slope of the roof.
5. Maps: Maps and globes use ratios and proportions to represent the size and distance of different locations. For example, a map may have a scale of 1 inch to 10 miles, which means that 1 inch on the map represents 10 miles in real life.

Test your knowledge with Upfunda Quiz!

1. In an office, the working hours are 9.30 to 5.30 PM and in between 30 minutes are spent on lunch. Find the ratio of office hours to the time spent for lunch.
2. If X : y : : y : z then the correct statement is
3. First, Second and third terms of a proportion are 5, 120 and 40. Then the fourth term is  Choose A) 960
4. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?