Chapter 5.2, Problem 26E

To determine

To describe and correct : The error in adding $-\frac{3}{7}$ and $\frac{2}{7}$ .

Answer to Problem 26E

The correct answer after adding $-\frac{3}{7}$ and $\frac{2}{7}$ is $-\frac{1}{7}$ .

Explanation of Solution

Given information: Describe and correct the error in adding $-\frac{3}{7}$ and $\frac{2}{7}$ .

Calculation: The given calculation is incorrect because, there is no use of LCM (Least common multiple), in the calculation. It can’t be added directly because, any fractional numbers should be added with the help of LCM.

Here is the correct calculation,

Since, $\frac{3}{7}$ is a negative number, and $\frac{2}{7}$ is a positive number.

Let’s finding the difference,

$\begin{array}{l}=-\frac{3}{7}+\frac{2}{7}\\ =\frac{-3+2}{7}\\ =-\frac{1}{7}\end{array}$ , Taking $7$ as the LCM (Least common multiple)

Negative sign has been used in the difference because, the number with negative sign is bigger than the number with positive sign. i.e. The sign of the bigger number should always be used.

Hence, The correct answer of adding $-\frac{3}{7}$ and $\frac{2}{7}$ is $-\frac{3}{13}$ .