Q13. - Algebra 1

Question

Graph each set of numbers

$\left\{\frac{7}{5}, -\frac{3}{5}, \frac{3}{4}, -\frac{6}{5}\right\}$

Step-by-Step Solution

Answer

The order of given set of real numbers is $-\frac{6}{5}<\frac{-3}{5}<\frac{3}{4}<\frac{7}{5}$.

Step-1. Apply the concept of the real number line.

Every real number can be represented by a unique point on the real number line. The point associated with the number is called a coordinate.

 

In the number line, the number 0 is called the origin. All the positive numbers or integers are represented on the right side of the origin, and the negative numbers or integers are represented on the left side of the origin. This line extends indefinitely at both ends and represents the integers in equal intervals.

 

It is used as a reference for comparing and ordering numbers. The numbers are represented in such a way that as we go towards right side, the numbers keep on increasing.

Step-2. Arrange the given set of real numbers in ascending order.

We will compare the given real numbers $\left\{\frac{7}{5},\frac{-3}{5},\frac{3}{4},-\frac{6}{5}\right\}$

Consider $-\frac{6}{5}=-1.2$. It is closer to –1 and in between $-2$ and –1.

Consider $-\frac{3}{5}=-0.6$. It is closer to –0.5 and in between –1 and 0.

Consider $\frac{3}{4}=0.75$. It is closer to 1and in between 0 and 1.

Consider $\frac{7}{5}=1.4$. It is closer to 1.5 and in between 1 and 2.

 

Now, real number line depicts integers in ascending order that is from smallest to largest.

 

So, smallest is $-\frac{6}{5}$ and largest is $\frac{7}{5}$.

Arranging the given set of real numbers in ascending order gives:

$-\frac{6}{5}<\frac{-3}{5}<\frac{3}{4}<\frac{7}{5}$

Step-3. Plot the given set of real numbers on the number line.

Construct a real number line. Mark the negative integers on the left of 0 and positive integers on the right of 0 with equal intervals.

 

Plot the set of real numbers $\left\{\frac{7}{5},\frac{-3}{5},\frac{3}{4},-\frac{6}{5}\right\}$ in such a way that the smallest comes to the left and largest to the right and in ascending order:

$-\frac{6}{5}<\frac{-3}{5}<\frac{3}{4}<\frac{7}{5}$

The resultant number line is as follows: