  ### Home > CCAA > Chapter 4 Unit 3 > Lesson CC2: 4.2.2 > Problem4-44

4-44.

Identify the mathematical property, operation, or idea that justifies each sequence of expressions below. Then find the value of the expression.

1. $7·2+4-2(7+3)$
$7·2+4-2(7)-2(3)$
$7·2-7(2)+4-2(3)$

Notice how the Distributive Property was used to change the first line into the second.
$\begin{equation} \begin{array}{c} 7\cdot2+4-2(7+3)\\ 7\cdot2+4-2(7){\color{blue}{\overset{\swarrow\searrow}{\color{black}{-}}}}2(3)\\ 7\cdot2-7(2)+4-2(3) \end{array} \end{equation}\\$

Two terms were moved using the Commutative Property of Addition. Keep in mind that subtraction is the same as adding a negative. Also, note that the term $2(7)$ became $7(2)$ through the Commutative Property of Multiplication.
$\begin{equation} \begin{array}{c} 7\cdot2+4-2(7+3)\\ 7\cdot2+\color{blue}{\underline{\color{black}{4-2(7)}}}{\color{blue}{\overset{\swarrow\searrow}{\color{black}{-}}}}2(3)\\ 7\cdot2-\color{blue}{\underline{\color{black}{7(2)+4}}}-2(3) \end{array} \end{equation}\\$

Simplify each term, then add them together. Circle the terms if it helps.
$7·2-7(2)+4-2(3)=$
$14-14+4-6=$

$-2$

1. $6·3+3·4-8$
$18+12-8$
$18-8+12$

Look at the differences between each line carefully. What was done to change the first line into the second? What property was used to move the underlined terms?

$\begin{equation} \begin{array}{c} 6\cdot3+3\cdot4-8\\ 18+\color{blue}{\underline{\color{black}{12-8}}}\\ 18-\color{blue}{\underline{\color{black}{8+12}}} \end{array} \end{equation}\\$

$18-8+12=22$
Make sure you identify mathematical properties, operations, and ideas that are used.

1. $3^2+5(1-3)+4·5+1$
$3^2+4·5+1+5(-2)$
$9+20+1-10$

Be very careful with this one. Multiple properties and operations are used in each line.

1. $(8+(-12))+10+2$
$8+(-12+10+2)$

Only one property is used in this one.