For example: \(\dfrac{2}{3},\dfrac{2}{7},\dfrac{4}{9}\) etc. are fractions.
For example: \(\dfrac{4}{5}\)
\(4\) is the numerator of the given fraction.
For example: \(\dfrac{5}{7}\)
\(7\) is the denominator of the given fraction.
1. Proper fraction:
For example: \(\dfrac{2}{3}\begin{matrix} \longrightarrow\text{Numerator}\\ \,\,\,\,\longrightarrow\text{Denominator} \end{matrix}\)
\(2\) is smaller than \(3\).
\(\therefore\;\;\dfrac{2}{3}\) is a proper fraction.
2. Improper fraction:
For example: \(\dfrac{5}{2}\begin{matrix} \longrightarrow\text{Numerator}\\ \;\;\,\longrightarrow\text{Denominator} \end{matrix}\)
\(5\) is larger than \(2\).
\(\therefore\;\;\dfrac{5}{2}\) is an improper fraction.
3. Mixed number:
For example: \(2\dfrac{1}{3}\)
In \(2\dfrac{1}{3}\), whole number \(=2\)
Proper fraction \(=\dfrac{1}{3}\)
\(\therefore\) \(2\dfrac{1}{3}\) is a mixed number.
4. Unit fraction:
For example: \(\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{8},\dfrac{1}{11}\) are unit fractions.
A \(\dfrac{3}{8}\)
B \(\dfrac{7}{4}\)
C \(\dfrac{1}{3}\)
D \(\dfrac{4}{5}\)
Step 1 Count the number of total parts in the figure and take this as the denominator of the fraction.
Step 2 Count the number of parts for which fraction is to be calculated in the figure and take this as the numerator.
Example : If fraction is asked for shaded portion then count the number of shaded parts for numerator.
In the example of given circle :
Shaded parts \(=3\)
Unshaded parts \(=5\)
Total number of parts = 8
Fraction for shaded parts:
Denominator = Total number of parts = 8
Numerator = Number of shaded parts = 3
\(\therefore\) The fraction representing shaded parts \(=\dfrac{3}{8}\)
Fraction for unshaded parts:
Denominator = Total number of parts = 8
Numerator = Number of unshaded parts = 5
\(\therefore\) The fraction representing the unshaded parts\(=\dfrac{5}{8}\)
NOTE : If the figure is not divided into equal parts, then first we need to divide it into equal parts.
For example:
The given figure is not divided into equal parts, so first we make all parts equal.
Now, the figure is divided into 8 equal parts.
Number of shaded parts \(=3\)
Total number of parts are taken as denominator and number of shaded parts are taken as numerator.
So, the fraction representing the shaded parts \(=\dfrac{3}{8}\)
A \(\dfrac{1}{4}\)
B \(\dfrac{5}{6}\)
C \(\dfrac{5}{8}\)
D \(\dfrac{3}{9}\)
In the given figure, all the parts are not equal.
So, first we make all parts equal.
Number of total parts are \(8\), so we take \(8\) as the denominator.
Number of shaded parts are \(5\), so we take \(5\) as the numerator.
So, the fraction representing the shaded parts \(=\dfrac{5}{8}\)
Hence, option (C) is correct.
Option C is Correct
For example:
\(\dfrac {1}{2}=\dfrac {2}{4}=\dfrac {4}{8}\) are equivalent fractions.
Multiply both numerator and denominator by the same non-zero whole number, like 2 in this case.
\(\Rightarrow\dfrac {1×2}{3×2}=\dfrac {2}{6}\)
The Greatest Common Factor of 2 and 6 is 2, so we divide both the numerator and the denominator by 2.
We get \(\dfrac{1}{3}\) which is same as the original fraction.
The new fraction \(\left(\dfrac{2}{6}\right)\) is the equivalent fraction of the original fraction.
Equivalent fraction of \(\dfrac {1}{3}=\dfrac {2}{6}\)
Though, \(\dfrac {1}{3}\) and \(\dfrac {2}{6}\) look different but they have the same value.
A \(\dfrac {9}{6}\)
B \(\dfrac {6}{9}\)
C \(\dfrac {12}{4}\)
D \(\dfrac {15}{8}\)
A unit fraction is a fraction in which the numerator is \(1\).
For example: \(\dfrac {1}{2},\dfrac {1}{3},\dfrac {1}{8},\dfrac {1}{11}\) are unit fractions.
Let us consider \(\dfrac {1}{b}\) as a unit fraction.
To represent \(\dfrac {1}{b}\) on a number line:
For example: Represent \(\dfrac {1}{5}\) on a number line.
Step 1 : Define the interval from \(0\) to \(1\).
Step 2 : Divide it into 5 equal parts.
Step 3 : Size of each part is \(\dfrac {1}{5}\).
Step 4 : By observing the number line, we can say that the distance from \(0\) to point \(\dfrac {1}{5}\) represents the unit fraction.
To represent the fraction \(\dfrac {a}{b}\) on a number line:
For example: Represent \(\dfrac {3}{4}\) on a number line.
Step 1: Define the interval from 0 to 1.
Step 2: Divide the interval into 4 equal parts.
Step 3 : The size of each part is \(\dfrac {1}{4}\).
Step 4: Thus, \(\dfrac {3}{4}\) represents the combined length of \(3\) parts.
Here,
\(\dfrac {0}{4}+\dfrac {1}{4} =\dfrac {1}{4}\)
\(\dfrac {1}{4}+\dfrac {1}{4} =\dfrac {2}{4}\)
\(\dfrac {1}{4}+\dfrac {1}{4}+\dfrac {1}{4} =\dfrac {3}{4}\)
\(\dfrac {1}{4}+\dfrac {1}{4}+\dfrac {1}{4}+\dfrac {1}{4} =\dfrac {4}{4}=1\)
Step 5: The resulting number line representation is:
A
B
C
D
Given fraction: \(\dfrac{1}{6}\)
Define the interval from \(0\) to \(1\) .
Divide it into 6 equal parts.
Size of each part is \(\dfrac{1}{6}\).
\(\dfrac{1}{6}\) represents the length of the first segment.
Hence, option (D) is correct.
Option D is Correct
We can understand the concept with the following example:
For example: Shade \(\dfrac{5}{6}\) part of the given rectangle.
First, we divide the given rectangle into \(6\) equal parts because the denominator is \(6\) and denominator represents the total parts.
Now, we shade \(5\) parts of the rectangle.
Shaded part represents \(\dfrac{5}{6}\) of the figure.
Shaded part represents \(\dfrac{5}{6}\) of the figure.
A \(\dfrac{2}{5}\)
B \(\dfrac{9}{4}\)
C \(\dfrac{4}{9}\)
D \(\dfrac{5}{9}\)
Divide the figure into equal parts as the denominator represents the total parts.
The figure is divided into \(9\) equal parts and there are \(4\) shaded parts.
The denominator represents the total parts of the figure, so the denominator is \(9\).
The numerator represents the number of shaded parts of the figure, so the numerator is \(4\).
Fraction representing the shaded parts
\(=\dfrac{4}{9}\)
Hence, option (C) is correct.
Option C is Correct
