Question

Write the fraction representing the shaded portion.

Answer 1

Hint: Write the “fraction of shaded portion $=\dfrac{\text{Numerator}}{\text{Denominator}}$ “

Here the numerator will be the area of the shaded portion and denominator will be equal to the total area. Assume a variable for the area of each triangle and calculate the total area of the shaded portion in terms of the variable.

Complete step-by-step answer:

We have to find the fraction representing the shaded portion. We know that “A fraction simply tells how many parts of a whole we have”. So, we have to find what fraction of total is the shaded portion. We can also say that we have to find what fraction of the total area is the shaded portion.

We know that fractions are calculated by finding its numerator and denominator. Numerator will be the part of the portion whose fraction is to be calculated and the denominator will be the whole thing whose parts or portions fraction is to be calculated.Here , we have to find the fraction of the shaded portion. 

So, Numerator = Area of the shaded portion and

Denominator = total area.

In the figure, we can see that all the smaller triangles are identified i.e. all of them will have equal area.Let the area of each smaller triangle = A.

So, total area $=4\times A$ as total triangles =4

And Area of shaded portion $2\times A$.........as No. of shaded $\Delta 'le=2$ 

Hence in our fraction,

Numerator = 2A and 

Denominator = 4A.

We know that, Fraction $=\dfrac{\text{Numerator}}{\text{Denominator}}$

Hence the required fraction $=\dfrac{2A}{4A}$ .

We know that if we divide both numerator and denominator by the same number, then the fraction doesn’t change. So, let us divide both the numerator and denominator of the obtained fraction by 2A. On dividing both numerator and denominator of fraction $\dfrac{2A}{4A}$ by 2A, we will get,

$\dfrac{2A}{4A}=\dfrac{\dfrac{2A}{2A}}{\dfrac{4A}{2A}} $

$\Rightarrow \dfrac{2A}{4A}=\dfrac{1}{2} $ 

Hence, the required fraction representing the shaded portion$=\dfrac{1}{2}$.

Note: As all the smaller triangles are identical, instead of finding the fraction in terms of area, we can also find the fraction in terms of number of triangles. As 2 triangles out of 4 triangles are shaded. 

Fraction of shaded portion $=\dfrac{2}{4}$ .

On dividing both numerator and denominator by 2, we will get,

$\Rightarrow \text{Fraction of shaded portion =}\dfrac{1}{2}$.