Fractions 1

In this article, we will learn about Fractions. The learning objectives are:

1. Understanding fractions
2. Writing fractions

1. Understanding Fractions

A fraction represents a part of a whole. The whole has to be divided into equal parts.

Example:

Let’s look at three whole pizzas. We need to split them into two equal slices. Which of the following has been cut into 2 equal slices?

    A                                     B                               C

Solution:

Pizza A has been cut into 2 equal slices. Pizza B and Pizza C are not cut into equal slices. 

Answer:

Pizza A

We can represent each slice of pizza in Pizza A as a fraction. Each slice is one-half of the whole pizza. One-half means 1 part out of 2 equal slices. This is represented as \(1\over2\). 

We can divide wholes into different equal parts. The following shows the fractions representing each slice of the pizzas.

Question 1: 

Which of the following shows \(\frac{1} {4}\) of the figure shaded?

1. A
2. B
3. C
4. D

Solution:

Only A is divided into 4 equal parts. Of which, 1 part out of 4 is shaded. 

Answer:

(1) A

Question 2: 

Which of the following shows \(\frac{1} {5}\) of the figure shaded?

1. A
2. B
3. C
4. D

Solution: 

Only D has been divided into 5 equal parts. Of which, 1 out of 5 equal parts is shaded. 

Answer:

(4) D

2. Writing Fractions

A fraction consists of a numerator and a denominator. The numerator refers to the part of a whole that you want. The denominator refers to the total number of equal parts a whole is split into.

Example: 

What fraction of each circle is shaded?

In this example, the numerator is the number of shaded parts while the denominator is the total number of equal parts.

Answer:

\(\frac{1} {4}\)

Answer:

\(\frac{2} {4}\)

Question 1: 

What fraction of the figure is shaded?

1. \(\frac{1} {2}\)
2. \(\frac{2} {4}\)
3. \(\frac{4} {6}\)
4. \(\frac{2} {6}\)

Solution:

The figure is divided into 6 equal parts. 2 parts are shaded. 

Answer:

(4) \(\frac{2} {6}\)

Question 2: 

What fraction of the figure is shaded?

1. \(\frac{2} {8}\)
2. \(\frac{2} {16}\)
3. \(\frac{3} {16}\)
4. \(\frac{3} {8}\)

Solution: 

The figure is divided into 16 equal parts. 3 parts are shaded. 

Answer:

(3) \(\frac{3} {16}\)

Question 3: 

What fraction of the figure is not shaded?

1. \(\frac{1} {2}\)
2. \(\frac{2} {4}\)
3. \(\frac{3} {4}\)
4. \(\frac{1} {4}\)

Solution: 

The figure is divided into 4 equal parts. 1 part is shaded and 3 parts are not shaded. 

Answer:

(3) \(\frac{3} {4}\)

Question 4: 

What fraction of the figure is not shaded?

1. \(\frac{4} {9}\)
2. \(\frac{5} {8}\)
3. \(\frac{5} {9}\)
4. \(\frac{1} {9}\)

Solution: 

The figure is divided into 9 equal parts. 4 parts are shaded and 5 parts are not shaded. 

Answer:

(3) \(\frac{5} {9}\)

Challenge yourself:

Question 1: 

What fraction of the figure is shaded?

1. \(\frac{3} {7}\)
2. \(\frac{3} {4}\)
3. \(\frac{5} {12}\)
4. \(\frac{7} {12}\)

Solution: 

To write a fraction, we need the figure to be divided into equal parts.

Let’s divide the figure further into equal parts and count.

Total number of parts \(= 12\)

Number of parts shaded \(= 5\)

Answer: 

(3)  \(\frac{5} {12}\)

Question 2:

The figure below is made up of 9 identical squares. How many more squares need to be shaded so that \(\frac{5} {9}\) of the whole figure is shaded?

1. 1
2. 2
3. 3
4. 5

Solution: 

3 out of 9 squares are shaded. So, \(\frac{3} {9}\) of the figure is shaded. We need to shade 2 more squares so that  \(\frac{5} {9}\) of the whole figure shaded. 

Answer:

(2) 2

In this article, we have learnt Fractions:

• Understanding Fractions
• Writing Fractions