Teaching Tips

The Relation between Fractions, Decimals and Percentages

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When do students first encounter fractions?

It’s probably when they see a 5/5 or 9/10 for a test.

They know that getting 9/10 is a matter of pride but when the concepts of fractions, decimals or percentages are introduced to them, they begin to lose interest.

So instead of independently explaining these concepts as abstract formulae or steps, subject matter experts suggest that we introduce the relation between the three. It helps to bring more clarity to students as a result they don’t see them separately.

In this article, we explain the concepts individually as well as their correlation with each other.

Fractions

A fraction is simply defined as a part of the whole. It can be 1 slice of a pizza, 2 hours in a week, 3 eggs from a dozen, etc. Let’s look at the following examples:

  1. Rohit, Anjali and Divya order a large pizza that has 8 slices. Rohit and Anjali have 2 slices each and Divya eats just 1 slice. So, if you look at the fraction:
    a. Rohit and Anjali individually ate 2/8th of the pizza, which means 2 out of 8 slices.
    b. Together they ate ½ the pizza.
    c. Divya ate ⅛th of it. 3/8th of the pizza was still left.
  2. Suppose you work in a company where every Saturday and Sunday is a holiday, you work 5/7th of the week.
  3. Your daily diet includes 3 eggs in a day, so you buy a carton of a dozen eggs for convenience. So this way, you know that you consume 3 eggs which is 3/12th of the carton.

A fraction, which is represented by a numerator and a denominator, is easily relatable when the concept is demonstrated through these simple real life situations. This way, children can visualize that the numerator represents the number of parts to be considered and the denominator is the total number of equal parts available.

Decimals

A decimal number is a number where the fraction part is denoted by digits after the decimal point. Decimals are used in situations which require more precision than whole numbers can provide.

Money is one such case. A packet of chips costs Rs. 10.50, where .50 is the decimal part.

Rs. 10.50 = Rs. (10 + 0.50) = Rs. 10 + Rs. 0.50

And we know, 50 paise is nothing but ½ a rupee.

Let’s consider a few more examples:

  1. Delhi temperature touches 47.8 degrees: We can write 47.8 = 47 + 0.8, where 0.8 = 8/10 or 4/5
  2. The pencil measures 5.20 cm: 5.20 = 5 + 0.20, where 0.20 = 20/100 or 1/5
  3. 0.049 parts of carbohydrate in milk: 0.049 = 49/1000

Here we see how decimals and fractions are related and interchangeable. We also look at the different place values up to which a decimal number can extend. The place value of decimals begin from tenths in example 1, go up to hundredths in example 3 and similarly, can go on.

Although at school we are taught how to round off decimal figures, it is important that children know about decimals and place values to understand the importance of precision and accuracy. Moreover, these concepts can be strengthened with the help of interesting learning aids.

See how 2.86 can be visualised using flats and rods:

Percentages

Percentage in literal terms means per cent, or per 100. One percent (1%) means 1 per 100. 50% means 50 per 100. At the outset we can see that percentages and fractions are closely related. Percentages are most commonly used to make comparisons easier.

For example, it is known that the population of India is 1.311 billion and that of Pakistan is 188.9 million. So how do we compare the literacy rates of both the countries when the populations have such a vast difference?

We compare it per hundred and therefore, the results tell us that the literacy rate of India is 74.04% while that of Pakistan is 66.6%. Which means that on an average, 74 out of every 100 Indian is a literate and 66 out of every 100 people in Pakistan are literates.

We can also present these percentage values as decimals and fractions:

74.04% =  0.7404 = (74 + 4/100) %

66.6% = 0.666 = (66 + 6/10) %

Similarly, we can compare countries, people, weather, etc., with respect to a whole lot of other parameters and get informative conclusions.

So fractions, decimals and percentage make processes smooth that are easy to understand. You can make use of learning aids like Cuemath teachers do to teach your children in a visualised manner.

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Meryl Vincent

Campaign Associate at Cuemath
Meryl is the resident blogger at Cuemath. She works with Cuemath teachers and students to bring out their math related stories. Apart from this, she also collaborates with the Curriculum team at Cuemath to bring out the fascinating side of math through articles and contests. You can contact her on meryl@cuemath.com for any blog related enquiry.

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