Fractions, Types, Shaded Diagrams & Real Life Applications

$\frac{4}{5},-\frac{7}{12},\frac{1}{2}$

Example 1. Fraction $\frac{1}{2}$
The numerator 1 is represented by the shaded box.
The denominator 2 is the total number of boxes.

So, the above diagram shows the 1 part out of 2 equal parts of the fraction $\frac{1}{2}$.

Example 2. Fraction $\frac{1}{3}$
The shaded box represents the numerator 1.
The denominator 3 is the total number of boxes.

So, the above diagram shows the 1 part out of 3 equal parts of the fraction $\frac{1}{3}$.

Example 3. Fraction $\frac{2}{4}$
So, here, total number of sectors in the circle = 4
and number of shaded sectors in the circle = 2

So, the above diagram shows the 2 parts out of 4 equal parts.

Example 4. Fraction $\frac{0}{3}$
Total number of boxes = 3
and number of shaded boxes = 0

So, the above diagram shows the 0 part out of 3 equal parts.

Example 5. Fraction $\frac{3}{3}$
Total number of boxes = 3
and number of shaded boxes = 3

So, the above diagram shows the 3 parts out of 3 equal parts.

Example 6. Fraction $\frac{4}{10}$
Total number of boxes = 10
and number of shaded boxes = 4

So, the above diagram shows the 4 parts out of 10 equal parts.

$\frac{7}{12},-\frac{3}{8},\frac{19}{21}$

$\frac{11}{5},-\frac{7}{2},\frac{85}{21}$

$2\frac{3}{5}$ here 2 represents the whole part and $\frac{3}{5}$ represents a proper fraction.

$\frac{1}{4},\frac{1}{7},\frac{1}{61}$
In $\frac{1}{4}$ , the numerator is 1 and denominator 4 which is a positive integer.

$\frac{3}{10},-\frac{1}{100},\frac{11}{1000}$

$\frac{1}{9},\frac{2}{9},\frac{7}{9}$
$\frac{1}{9},\frac{2}{9}$ and $\frac{7}{9}$ have the same denominators i.e. 9, so they are like fractions.

$\frac{7}{9},\frac{1}{4},\frac{6}{11},\frac{5}{8}$
$\frac{7}{9},\frac{1}{4},\frac{6}{11}$ and $\frac{5}{8}$ have different denominators i.e. 9, 4, 11 and 8 respectively, so they are unlike fractions.

$\frac{2}{\frac{5}{7}},\frac{7}{\frac{5}{\frac{6}{7}}}$

Example 1: Write equivalent fractions of $\frac{4}{9}$
Multiply both numerator and denominator by 2:
$\frac{4}{9}\times \frac{2}{2}=\frac{8}{18}$
Multiply both numerator and denominator by 5:
$\frac{4}{9}\times \frac{5}{5}=\frac{20}{45}$
∴ $\frac{8}{18}$ and $\frac{20}{45}$ are equivalent fractions.

Example 2: Check $\frac{1}{3}$ and $\frac{3}{9}$ are equivalent fractions.
Multiply both numerator and denominator by 1:
$\frac{1}{3}\times \frac{1}{1}=\frac{1}{3}$
Multiply both numerator and denominator by 2:
$\frac{1}{3}\times \frac{2}{2}=\frac{2}{6}$
Multiply both numerator and denominator by 3:
$\frac{1}{3}\times \frac{3}{3}=\frac{3}{9}$
∴ $\frac{1}{3}$ becomes equal to $\frac{3}{9}$ when multiplied by 3.
Hence, $\frac{1}{3}$ and $\frac{3}{9}$ are equivalent fractions.

Convert the improper fraction $\frac{9}{4}$ to mixed fraction.
Step 1: Divide the numerator 9 by the denominator 4.

quotient = 2
remainder = 1

Step 2: Write the quotient 2 as the whole part, 1 as the numerator and 4 as the denominator of the fraction part.
∴ mixed fraction = $2\frac{1}{4}$

Convert $3\frac{4}{5}$ into improper fraction.
Here, 3 is the whole part and $\frac{4}{5}$ is the proper fraction with 4 as numerator and 5 as the denominator.
Step 1: Multiply 3 by 5 which is equal to 15.
Step 2: Add numerator 4 of the proper fraction part to the number 15 which is obtained in step 1, which is equal to 19.
Step 3: The new fraction with numerator equal to the number obtained in step 2, which is 19 and the denominator same as that of proper fraction, which is 5.

∴ $\frac{19}{5}$ is an improper fraction.