Question

Simplify each expression

$4\left(0.2m-0.3n\right)-6\left(0.7m-0.5n\right)$

Short answer

$4\left(0.2m-0.3n\right)-6\left(0.7m-0.5n\right)$is simplified to localid="1647354375240" $2\left(-1.7m+0.9n\right)$

Step-by-step solution

- Write properties of real numbers 

Properties of real numbers are written in following table:

For any real numbers a, b, and c:
Property	Addition	Multiplication
Commutative	a+b=b+a	$a·b=b·a$
Associative	$\left(a+b\right)+c=a+\left(b+c\right)$	$\left(a·b\right)·c=a·\left(b·c\right)$
Identity	a+0=a=0+a	$a·1=a=1·a$
Inverse	$a+\left(-a\right)=0=\left(-a\right)+a$	If $a\ne 0$, then $a·\frac{1}{a}=1=\frac{1}{a}·a$
Distributive	$a\left(b+c\right)=ab+ac\text{and}\left(b+c\right)a=ba+ca$.

- Simplify by grouping same variables

To simplify given equation, first use distributive property then commutative property of addition then distributive property to group coefficients of same variable as shown below

$\begin{array}{c}4\left(0.2m-0.3n\right)-6\left(0.7m-0.5n\right)=0.8m-1.2n-4.2m+3n\\ =0.8m-4.2m-1.2n+3n\\ =\left(0.8-4.2\right)m+\left(-1.2+3\right)n\end{array}$

- Use distributive property 

Firstly simplify parentheses then take out common factor of both terms as shown below

$\begin{array}{c}\left(0.8-4.2\right)m+\left(-1.2+3\right)n=-3.4m+1.8n\\ =2\left(-1.7m+0.9n\right)\end{array}$