Mathematical Operations of Numbers and Simplifying Algebraic Expressions

Section A.: Mathematical Operations of Numbers

1.)

8+((12+5) x 4)/2=
8+(17x4)/2=
8+68/2=
8+34=
42

2.)

((3+4)²+4)-2=
(7²+4)-2=
(49+4)-2=
53-2=
51

3.)

((12+7)+(8/4)²)
(19)+(2)²
19+4
23

4.)

½ + ¼ - ⅓=
6/12+3/12-4/12=
9/12-4/12=
5/12

5.)

2/3 x 3/5 =
Multiply straight across
2/3 x 3/5 = 6/15
Find common denominator
Reduce to lowest term
6/15 ÷ 3/3 = 2/5

6.)

⅓ ÷ ½ =
Multiply by reciprocal
⅓ x 2/1=
2/3

7.)

3/2 ÷ ( 1/5 + 6/10) =
3/2 ÷ (2/10 + 6/10) =
3/2 ÷ 8/10 =
Multiply by reciprocal
3/2 x 10/8 = 30/16 = 15/8 = 1 7/8

Section B.: Simplifying Algebraic Expressions

1.)

2x + 3x - 5x + x =
5x - 5x + x =
0 + x = x 2.)

2(6x + 5) =
2(6x) + (2x5) =
12x + 10 =

3.)

(14x - 7) /7 =
14x - 7 ÷ 7 =
14x ÷ 7 = 2x -7 ÷ 7 = -1
2x - 1

4.)

-(-15x) - 3x =
15x - 3x =
12x

5.)

5(3x+4) - 4 =
15x + 20 - 4 =
15x + 16 =

6.)

5(3x-2)+12x =
15x -10+12x =
27x - 10 =

7.)

4(2y-6)+3(5y+10) =
8y-24+15y+30 =
23y-24+30 =
23y+6=

8.)

(x+1) (x-2) =
Multiply the first 2, outside 2, inside 2, last 2 xx - 2x + 1x - 2 = xx - 2x + x - 2 =