# The secret to understanding fractions

By Arindam Nag, Founder, Learnhive

So your child can easily share half his cake or a third of his chocolate, but when confronted with adding 1/2 + 1/3, comes up with 2/5 ? Welcome to one of the most common mistakes that children (and perhaps even grown ups) tend to do while dealing with fractions.

## Why are fractions so important?

World’s resources are limited and they have to be shared. We use fractions to do that. Fractions is the basis for mathematical concepts such as rational numbers, percentages, ratios, and proportions. Understanding of fractions and decimals is crucial for calculating simple and compound interest problems. Solving algebraic expressions requires knowldege of fractions. In Geometry, calculation of area and volume for any shape other than a square or rectangle requires knowledge of fractions. Fractions are an integral part of our day to day lives.

## When do children learn about fractions?

In most curricula, the concept of fractions is introduced as early as Grade 2. It is repeated with increasing complexity every year until about Grade 7. The notation to represent fractions and categorization into different types of fractions is taught in Grade 4. Operations on fractions is done in Grades 5 and 6. Decimal notation of fractions is introduced around Grade 5.

## What are the common mistakes with use of proper fractions?

The concept is usually introduced to children by showing them how to share a cake or pizza or chapati (Indian bread) which is pretty well comprehended by children. In this form, fraction is represented as part of a whole, a proper fraction.

Difficulty usually creeps in when the number notation is introduced. Is 1/3 more or less than 1/4? Children may divide something  like a sheet of paper into 3 parts and another one into 4 parts and count these parts and incorrectly say that 1/4 is greater than 1/3. What is important to explain is that they need to compare the resultant (as in size) and see which one is bigger or smaller.

When you compare natural numbers, you are comparing how many (count). How many?

When you compare fractions, you compare how much (size or amount). How much?

A similar complication arises while adding proper fractions. The most common mistake done by children is to add the numerators and the denominators separately treating them similar to natural numbers. Once the how many versus how much is well explained, they can then easily grasp why it is necessary to convert the various fractions being added to like fractions (denominator is same) . Multiplication throws up another interesting challenge. When you multiply natural numbers, the result is larger. Multiplying proper fractions gives you a smaller result.

## How to explain improper and mixed fractions?

Improper (3/2) and mixed (1 1/2) fractions are explained best by giving another definition of fraction: as part of a collection. You have 3 slices of cake. How would you divide that amongst 2 siblings? Intuitively they know that can share one slice each and the third slice needs to be divided equally amongst them.

So, sound understanding of fractions is absolutely essential for children since not only does it form a pivotal basis for many of the other math topics, it is something they will use in their everyday lives.

What are other misconceptions have you seen children having with fractions?