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?
- \(\frac {\; 1 \;} {\; 2 \;}\)
- \(\frac {\; 1 \;} {\; 3 \;}\)
- \(\frac {\; 1 \;} {\; 4 \;}\)
- \(\frac {\; 1 \;} {\; 5 \;}\)
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?
- \(\frac {\; 1 \;} {\; 6 \;}\)
- \(\frac {\; 2 \;} {\; 6 \;}\)
- \(\frac {\; 4 \;} {\; 6 \;}\)
- \(\frac {\; 5 \;} {\; 6 \;}\)
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?
- \(\frac {\; 1 \;} {\; 8 \;}\)
- \(\frac {\; 3 \;} {\; 8 \;}\)
- \(\frac {\; 5 \;} {\; 8 \;}\)
- \(\frac {\; 7 \;} {\; 8 \;}\)
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:
- Understanding the simplest form
- 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 \(\frac {\; 3 \;} {\; 4 \;}\)?
- \(\frac {\; 4 \;} {\; 8 \;}\)
- \(\frac {\; 8 \;} {\; 12 \;}\)
- \(\frac {\; 13 \;} {\; 16 \;}\)
- \(\frac {\; 15 \;} {\; 20 \;}\)
Solution:
Answer:
(4) \(\frac {\; 15 \;} {\; 20 \;}\)
Question 8:
Which of the following is equivalent to \(\frac {\; 2 \;} {\; 12 \;}\)?
- \(\frac {\; 1 \;} {\; 6 \;}\)
- \(\frac {\; 2 \;} {\; 6 \;}\)
- \(\frac {\; 3 \;} {\; 6 \;}\)
- \(\frac {\; 4 \;} {\; 6 \;}\)
Solution:
Answer:
(1) \(\frac {\; 1 \;} {\; 6 \;}\)
Question 9:
Which of the following is equivalent to \(\frac {\; 4 \;} {\; 6 \;}\)?
- \(\frac {\; 1 \;} {\; 3 \;}\)
- \(\frac {\; 3 \;} {\; 7 \;}\)
- \(\frac {\; 8 \;} {\; 12 \;}\)
- \(\frac {\; 14 \;} {\; 16 \;}\)
Solution:
Answer:
(3) \(\frac {\; 8 \;} {\; 12 \;}\)