7.1. Recalling Ratios and Percentages

We know, ratio means comparing two quantities. A basket has two types of fruits, say, 20 apples and 5 oranges. Then, the ratio of the number of oranges to the number of apples = 5 : 20.

A ratio is a way to compare two quantities. In this case, we compare the number of oranges to the number of apples. With 5 oranges and 20 apples, we say the ratio is 5:20, which simplifies to 1:4. This means that for every 1 orange, there are 4 apples.

Think of a recipe that calls for 1 cup of sugar and 4 cups of flour. The ratio of sugar to flour is 1:4. If you double the recipe, you'll have 2 cups of sugar and 8 cups of flour, but the ratio remains the same.

The comparison can be done by using fractions as, 5/20 = 1/4. The number of oranges is 1/4 of the number of apples. In terms of ratio, this is 1 : 4, read as, “1 is to 4”.

Ratios can also be expressed as fractions. Here, we see that there are 5 oranges out of 20 total fruits, which can be simplified to the fraction 1/4. This fraction tells us that the number of oranges is one fourth of the number of apples.

If a class has 10 boys and 40 girls, the ratio of boys to girls is 10:40, which simplifies to 1:4. This tells you that for every boy, there are four girls in the class.

This comparison can also be done using percentages. There are 5 oranges out of 25 fruits. By unitary method: So percentage of oranges is (5/25) x 100 = 20%.

Percentages provide another way to compare quantities. Here, if there are 5 oranges out of a total of 25 fruits, we can calculate the percentage of oranges by dividing the number of oranges by the total number of fruits and multiplying by 100. This gives us 20%, meaning 20% of the fruits in the basket are oranges.

Imagine you have a box of 100 chocolates. If 20 chocolates are dark chocolate, then the percentage of dark chocolates is (20/100) x 100 = 20%. This helps you understand what fraction of the total is made up of dark chocolates.

Since the basket contains only apples and oranges, So, percentage of apples + percentage of oranges = 100 or percentage of apples + 20% = 100 or percentage of apples = 100 – 20 = 80.

In a situation where you have only two types of items, the total of their percentages must equal 100%. So if the percentage of oranges is 20%, the percentage of apples must be 100% - 20% = 80%. This is useful for understanding how two parts make up a whole.

If you and your friend have a collection of 50 stickers where you have 30 and your friend has 20, you can easily see that your share, 30 stickers, is 60% (30/50 * 100) of the total collection.

Example: A picnic is being planned in a school for Class VII. Girls are 60% of the total number of students and are 18 in number.

In this example, 60% of the total students are girls. When we know that there are 18 girls, we can use this information to find out how many total students there are. If 60% represents 18 girls, we can determine the total number by setting up the equation where 60% of the total number equals 18.

If in a class of 30 students, 60% are girls, we can calculate that there are 18 girls. Conversely, if we see 18 girls, knowing they comprise 60% of the class allows us to find out that the total class size is 30.

The picnic site is 55 km from the school and the transport company is charging at the rate of ₹12 per km.

To find out the total cost of transport for the picnic, we multiply the distance to the picnic site (55 km) by the rate charged by the company (₹12 per km). This kind of calculation helps budget for events like school picnics realistically.

If a taxi service charges ₹10 per kilometer and you need to travel 10 km, your total fare will be ₹10 x 10 = ₹100. Planning a school field trip follows similar budgeting where distances and costs are calculated to ensure everything fits within the budget.

The total cost of refreshments will be ₹4280. Can you tell the ratio of girls to boys in the class?

In planning events like picnics, knowing the total budget and how many students are involved helps understand and manage costs for food and activities. Here, we would compare the number of girls to the boys once we determine how many boys are there using the total student count derived from the earlier percentage calculations.

If you are throwing a birthday party and have a total budget of ₹5000, and you know food costs ₹2500, you can easily determine how much money you have left to spend on games and decorations.

--