Fractions Types, Representation With Diagrams And Conversions

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

Represent fraction $\frac{2}{4}$ in a circle.

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.

$\frac{1}{2}$

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 $\frac{1}{2}$ .

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 $\frac{1}{3}$ .

$\frac{0}{3}$

Total number of boxes = 3

and number of shaded boxes = 0

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

$\frac{3}{3}$

Total number of boxes = 3

and number of shaded boxes = 3

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

$\frac{4}{10}$

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.

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

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.

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.