Question

Identify the mathematical property, operation, or idea that justifies each sequence of expressions below. Then find the value of the expression.
a.
7⋅2+4−2(7+3)
7⋅2+4−2(7)−2(3)
7⋅2−7(2)+4−2(3)
b.
6⋅3+3⋅4−8
18+12−8
18−8+12
c.
3^2+5(1−3)+4⋅5+1
3^2+4⋅5+1+5(−2)
9+20+1−10
d.
(8+(−12))+10+2
8+(−12+10+2)

Answer 1

Answer:

a) Distributive Property of Multiplication, b) Prioritizing the multiplication, c) Solving the Parentheses first and Reordering the expression d) Grouping the numbers that cancel each other

Step-by-step explanation:

On these expressions below, we have some ways to proceed with this resolution.

a) Distributive Property on Multiplication made possible the distribution of factor -2 (line 1)

$a.\\7*2+4-2(7+3)\\7*2+4-2(7)-2(3)\\7*2-7(2)+4-2(3)\\14-14+4-6=-2$

b) Prioritizing the multiplication on line 1. By following the PEMDA acronym.

Parentheses, Exponents, Multiplication, Division, Adition.

$b.)6*3+3*4-8\:\:line\:1\\18+12-8\\18-8+12=22$

c) Solve the Parentheses first and Reorder the expression

$c.)\\3^2+5(1-3)+4*5+1\:line\: 1\\3^2+4*5+1+5(-2)\:line\:2\\9+20+1-10=20$

d) Grouping the numbers that cancel each other

$d.)\\(8+(-12))+10+2\\8+(-12+10+2)=8+(0)=8$