Session 1: What are Fractions? – Definition, Representation, Number line, Interactives and Examples

We know the power of food. Through food, we can share our culture and heritage. Food not only connects us all, but it truly brings out the best in us. It allows people from all around the globe to interact, grow, and of course, eat together.  

Did you know that cooking and baking is full of fractions? Chefs need to know fractions to bake and prepare items on a restaurant menu. They must also know how to double, triple, and sometimes half measurements on recipes. This means they need to understand fractions. For example, if the recipe provides an ingredient list for 36 cookies, but you only want to make nine cookies. In this case, you need to quarter each ingredient. So, if the recipe requires two teaspoons of baking powder, you only need \(\frac{1}{2}\) a teaspoon because 2÷4=\(\frac{1}{2}\).

In this lesson, we will recall, in brief, what we have learnt about fractions in the earlier classes.

What is a Fraction?

A fraction is a part of a whole. It describes the relationship between a part of something and the whole thing. A fraction has two numbers separated by a fraction bar. The top number is called the numerator and tells you how many parts there are out of the whole. The bottom number is the denominator. It tells you how many parts the whole has been divided into.

Representing Fraction

A fraction can be represented in different ways. For example, fraction \(\frac{1}{6}\) can be represented by each of the following pictorial representations.

A fraction also names part of a group. In the figure given below, three out of ten balloons are green. That’s one way of describing the fraction, but we can also describe it using numbers. The numerator would be three as there are three green balloons. There are ten balloons in total, so the denominator of this fraction would be ten. So, using numbers, there are \(\frac{3}{10}\) green balloons.

DID YOU KNOW? One of the earliest civilizations to write out fractions was the Egyptians. They had a base-ten writing system based on hieroglyphs from around 3000 BC. Hieroglyphs are little pictures representing words. They placed a mouth-like symbol that means “part” over the number to turn a number into a fraction. So, placing the mouth symbol over the number 2 meant \(\frac{1}{2}\). The Egyptians combined several fractions to represent fractions with a numerator other than one.

Representing Fractions on a Number Line

In the previous class, we have learnt how to represent whole numbers on a number line. To represent whole numbers on a number line, we draw a straight line and mark the points at an equal distance.

We can show fractions too on a number line. To represent \(\frac{3}{8}\) on the number line we first, look at the denominator. The denominator is 8. So, divide the section of the number line between 0 and 1 into eight equal parts. Each part represents \(\frac{1}{8}\).

Note: When dividing up the whole, draw 1 fewer line than the number shown in the denominator. 

The numerator is 3. So, we start at 0 and count forward three parts.

We mark a point. This point represents \(\frac{3}{8}\).

Steps to Represent Fraction on a Number Line

In summary, we can use the following steps to represent a fraction on a number line:

Step 1: Divide the number line between 0 and 1 into the number of parts of equal size shown by the denominator. 

Step 2: Starting at 0, count forward the number of parts shown by the numerator.

Step 3: Mark the point on the number line.

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What are Fractions? – Examples

Example 1

Ritika and her mom are at a pet store. The pet store has 18 pets. One-third of the pets are cats. Three are hamsters, and the rest are dogs. How many cats are there?

Here the fraction \(\frac{1}{3}\) means one part out of three.

So, \(\frac{1}{3}\) of 18 pets=\(\frac{1}{3}\)×18=6.

Hence, there are 6 cats in the pet store.

Example 2

Represent \(\frac{1}{6}\) on a number line.

First of all, we need to divide the number line between 0 and 1 into 6 equal parts, and the first part of the six parts will represent \(\frac{1}{6}\) on the number line.

Remember this!

• A fraction is a number representing a part of a whole. 
• The number above the bar in a fraction is called a numerator; it names the number of parts being considered.
• The number below the bar in a fraction is called a denominator; it names the total number of equal parts.
• A fraction can be expressed in the form of \(\frac{a}{b}\), where a, b are whole numbers and b≠0.