Question

Add the following expressions using both the horizontal method and column method:

$2r-3s+t$ and $4r+4s-3t$

Answer 1

Step 1: Adding the algebraic expression by the horizontal method

Horizontal method: Taking care of signs, write all expressions in a horizontal line and group like terms together. Now, add these like terms and get the required sum.

We have $2r-3s+t$ and $4r+4s-3t$

Now,

$$\begin{gathered} (2r-3s+t)+(4r+4s-3t)=2r-3s+t+4r+4s-3t \\ =2r+4r-3s+4s+t-3t \\ =(2+4)r+(-3+4)s+(1-3)t \\ =6r+s+(-2)t \\ =6r+s-2t \end{gathered}$$

Step 2: Adding the algebraic expression by the column method

Column method: Write each expression in separate lines such that their like terms lie in the same vertical column. Taking care of signs, add each column.

$$\begin{gathered} 2r-3s+t \\ +4r+4s-3t \\ \_\_\_\_\_\_\_\_\_\_\_\_\_ \\ 6r+s-2t \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \end{gathered}$$

Hence, the required sum is $6r+s-2t$.