Fractions

Fraction is used to represent part of a whole.

For example, the circle shown is divided into 3 equal parts. 

1 out of 3 parts is shaded. 

\(\frac {1}{3}\) of the figure is shaded. 

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Question 1:

What fraction of the figure is shaded?

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

Solution:

The circle is divided into 4 equal parts. 

1 out of 4 parts are shaded. 

\(\frac {\; 1 \;} {\; 4 \;}\) of the figure is shaded. 

Answer: 

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

Question 2:

What fraction of the figure is shaded?

1. \(\frac {\; 1 \;} {\; 6 \;}\)
2. \(\frac {\; 2 \;} {\; 6 \;}\)
3. \(\frac {\; 4 \;} {\; 6 \;}\)
4. \(\frac {\; 5 \;} {\; 6 \;}\)

Solution: 

The circle is divided into 6 equal parts. 

4 out of 6 parts are shaded. 

\(\frac {\; 4 \;} {\; 6 \;}\) of the figure is shaded. 

Answer:

(3) \(\frac {\; 4 \;} {\; 6 \;}\)

Question 3: 

What fraction of the figure is not shaded?

1. \(\frac {\; 1 \;} {\; 8 \;}\)
2. \(\frac {\; 3 \;} {\; 8 \;}\)
3. \(\frac {\; 5 \;} {\; 8 \;}\)
4. \(\frac {\; 7 \;} {\; 8 \;}\)

Solution: 

The circle is divided into 8 parts. 

3 out of 8 parts are not shaded. 

\(\frac {\; 3 \;} {\; 8 \;}\) of the figure is not shaded. 

Answer: 

(2) \(\frac {\; 3 \;} {\; 8 \;}\)

In this article, the learning objectives are:

1. Understanding the simplest form
2. Finding equivalent fractions

1. Understanding The Simplest Form

A fraction is in its simplest form if the numerator and the denominator cannot be divided by the same number any further.

Circle A	Circle B	Circle C
\(\frac {\; 1 \;} {\; 2 \;}\)	\(\frac {\; 2 \;} {\; 4 \;}\)	\(\frac {\; 3 \;} {\; 6 \;}\)

Question 1: 

Express \(\frac {\; 6 \;} {\; 24 \;}\) in its simplest form.

Solution:

          OR            

Answer:
\(\frac {\; 1 \;} {\; 4 \;}\)

Question 2: 

Express \(\frac {\; 5 \;} {\; 15 \;}\) in its simplest form.

Solution: 

Answer:

\(\frac {\; 1 \;} {\; 3 \;}\)

Question 3: 

Express \(\frac {\; 3 \;} {\; 18 \;}\) in its simplest form.

Solution:

Answer:

\(\frac {\; 1 \;} {\; 6 \;}\)

Question 4: 

Express \(\frac {\; 6 \;} {\; 10 \;}\) in its simplest form.

Solution: 

Answer:

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

Question 5: 

Express \(\frac {\; 12 \;} {\; 15 \;}\) in its simplest form.

Solution: 

Answer:

\(\frac {\; 4 \;} {\; 5 \;}\)

Question 6: 

Express \(\frac {\; 8 \;} {\; 20 \;}\) in its simplest form.

Solution: 

Answer:

\(\frac {\; 2 \;} {\; 5 \;}\)

2. Finding Equivalent Fractions

Equivalent fractions are fractions with different numerators and denominators but they represent the same value or proportion of a whole.

Circle A	Circle B
\(\frac {\; 1 \;} {\; 3 \;}\)	\(\frac {\; 2 \;} {\; 6 \;}\)

The areas shaded in both circles are exactly the same. 

Hence, 13 and 26 are equivalent fractions.

\(\frac {\; 1 \;} {\; 2 \;}\)	\(\frac {\; 2 \;} {\; 4 \;}\)	\(\frac {\; 4 \;} {\; 8 \;}\)

Equivalent fractions when expressed in its simplest form are the same. 

Question 1: 

What is the missing number?

\(\frac {4} {10}=\frac {2}{?}\)

Solution: 

The missing number is 5.

Answer:

5

Question 2: 

What is the missing number?

\(\frac {9} {12} = \frac{3}{?}\)

Solution:

The missing number is 4.

Answer:

4

Question 3: 

What is the missing number?

\(\frac {12} {18}=\frac{4}{?}\) 

Solution:

The missing number is 6.

Answer:

6

Question 4: 

What is the missing number?

\(\frac {3} {5}=\frac{?}{10}\)

Solution: 

The missing number is 6. 

Answer:

6

Question 5: 

What is the missing number?

\(\frac {3} {4}=\frac{?}{12}\)

Solution:

The missing number is 9.

Answer:

9

Question 6: 

What is the missing number?

\(\frac {2}{3}=\frac{?}{18}\)

Solution:

The missing number is 12. 

Answer:

12

Question 7: 

Which of the following is equivalent to \(\frac {\; 3 \;} {\; 4 \;}\)?

1. \(\frac {\; 4 \;} {\; 8 \;}\)
2. \(\frac {\; 8 \;} {\; 12 \;}\)
3. \(\frac {\; 13 \;} {\; 16 \;}\)
4. \(\frac {\; 15 \;} {\; 20 \;}\)

Solution: 

Answer:

(4) \(\frac {\; 15 \;} {\; 20 \;}\)

Question 8: 

Which of the following is equivalent to \(\frac {\; 2 \;} {\; 12 \;}\)? 

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

Solution: 

Answer: 

(1) \(\frac {\; 1 \;} {\; 6 \;}\)

Question 9: 

Which of the following is equivalent to \(\frac {\; 4 \;} {\; 6 \;}\)? 

1. \(\frac {\; 1 \;} {\; 3 \;}\)
2. \(\frac {\; 3 \;} {\; 7 \;}\)
3. \(\frac {\; 8 \;} {\; 12 \;}\)
4. \(\frac {\; 14 \;} {\; 16 \;}\)

Solution:

Answer:

(3) \(\frac {\; 8 \;} {\; 12 \;}\)