Question

Arrange the given expression vertically and add them.

(1) 11x, 6x, –2x
(2) –y², 13y², –5y²
(3) 4a²bc, –9bca², 14cba²
(4) $\frac{1}{2}a{x}^2,\frac{3}{2}a{x}^2,-2a{x}^2$

Answer 1

(1) We can arrange the terms vertically as:
$\begin{array}{cc}& 11x\\ +& 6x\\ +& -2x\\ & \overline{15x}\end{array}$ (Because the sum of 11 and 6 is 17 and the sum of 17 and (–2) is 15)

(2) We can arrange the terms vertically as:
$\begin{array}{cc}& -y^2\\ +& 13y^2\\ +& -5y^2\\ & \overline{7y^2}\end{array}$ (Because the sum of (–1) and 13 is 12 and the sum of 12 and (–5) is 7)

(3) We can arrange the terms vertically as:
$\begin{array}{cc}& 4a^{2}bc\\ +& -9a^{2}bc\\ +& 14a^{2}bc\\ & \overline{9a^{2}bc}\end{array}$ (Because the sum of 4 and (–9) is (–5) and the sum of (–5) and 14 is 9)

(4) We can arrange the terms vertically as:
$\begin{array}{cc}& \frac{1}{2}a{x}^2\\ +& \frac{3}{2}a{x}^2\\ +& -2a{x}^2\\ & \overline{0}\end{array}$ (Because the sum of $\frac{1}{2}$ and $\frac{3}{2}$ is 2, i.e., $\frac{1}{2}+\frac{3}{2}=\frac{1+3}{2}=\frac{4}{2}=2$, and the sum of 2 and (–2) is 0)