Question

Solve

$1-2+3-4+5-6+7-8+9-10$

Answer 1

Finding the value of given expression:

First, put together all the terms containing the positive sign and add them.

$$\begin{gathered} 1+3+5+7+9 \\ =4+5+7+9 \\ =9+7+9 \\ =16+9 \\ =25 \end{gathered}$$

Also, put together all the terms containing the negative sign and add them and assign the negative sign to the result.

$$\begin{gathered} (-2)+(-4)+(-6)+(-8)+(-10) \\ =(-6)+(-6)+(-8)+(-10) \\ =(-12)+(-8)+(-10) \\ =(-20)+(-10) \\ =-30 \end{gathered}$$

Now, find the difference between the absolute value of the integers obtained and assign to it the sign of the integer having the greater absolute value. i.e.,

$\left|25\right|=25$ and $\left|-30\right|=30$

$25-30=-5$

Hence, $1-2+3-4+5-6+7-8+9-10=-5$