Properties & Mental Math
Distributive Property
Simplifying Expressions
Solving Equations
Applications
100
Use the identify property to reduce this fraction:
11.2/7
(11.2/8)=(10/10)=(112/8)=(56/4)=(28/2)=14
100
Use the distributive property to evaluate
5(204)
5(204)=5(200+4)=1000+20=1020
100
Simplify.
5x-9-x+2
5x-9-x+2=
5x-x-9+2=
4x-7
100
Solve.
x+16=6
x+16=6
x+16-16=6-16
x=-10
100
The difference of 17 and x is four. Solve for x.
17-x=4
17-17-x=4-17
-x=-13
-x(-1)=-13(-1)
x=13
200
How would you rearrange the following problem to make computation easier, and what property did you use to do so? Then evaluate the expression.
57+28+13
57+28+13=
57+13+28
by the commutative property of addition
70+28=98
200
Write an expression equivalent to
4(3x-2)
Simplify that expression.
4(3x-2)=4*3x-4*2=12x-8
200
Simplify.
2-3(x+1)
2-3(x+1)=
2+(-3)*x+(-3)*1=
2-3x-3=
2-3-3x=
-1-3x
200
Solve.
-9+t=16
-9+t=16
-9+9+t=16+9
t=7
hold
200
Find the area of this figure.
(8(7-c))/2=
8/2*(7-c)/1=
4*(7-c)/1=
4(7-c)=
4*7-4*c=
28-4c
28 - 4c square units
300
How would you rearrange the following problem to make computation easier, and what property did you use to do so? Then evaluate the expression.
-5(19)(20)
-5(19)(20)=
-5(20)(19)
by the commutative property of multiplication
-100(19)=-1900
300
Write an expression equivalent to
-2(x+4)
Simplify that expression.
-2(x+4)=
-2*x+(-2)(4)=
-2x+(-8)=
-2x-8
300
3(u+1)+4u+1
3(u+1)+4u+1=
3*u+3*1+4u+1=
3u+3+4u+1=
3u+4u+3+1=
7u+4
300
Solve.
-54=-3y
(-54)/-3=(-3y)/(-3)
(-54)/-3=y
18=y
300
An engineer receives a promotion that includes a raise of $4,500 in her annual salary. Her new salary is $50,750. What was her salary before the promotion?
Write an algebraic equation to represent this situation, then solve your equation.
s+4,500=50,750
s+4,500-4,500=50,750-4,500
s=46,250
400
How would you rearrange the following problem to make computation easier, and what property did you use to do so? Then evaluate the expression.
4.7+(2.3+2.5)
4.7+(2.3+2.5)=
(4.7+2.3)+2.5
by the associate property of addition
7.0+2.5=9.5
400
Write an expression equivalent to
(y-8)5
Simplify that expression.
(y-8)5=
y*5-8*5=
5y-40
400
Simplify.
8a-2(7a-3)
8a-2(7a-3)=
8a+(-2)(7a)-(-2)(3)=
8a+(-14a)-(-6)=
8a-14a+6=
-6a+6
400
Solve.
x/8=4
x/8=4
(x/8)8=4*8
(x/8)(8/1)=4*8
(8x)/8=32
x=32
400
You divide a stack of fliers for a craft fair into 6 smaller stacks for volunteers to distribute. Each smaller stack contains 15 fliers. What is the total number of fliers distributed?
Write an algebraic equation to represent this situation, then solve your equation.
f/6=15
where f = the total number of fliers
(f/6)6=15*6
f/6*6/1=30*3
f=90
90 fliers in total
500
How would you rearrange the following problem to make computation easier, and what property did you use to do so? Then evaluate the expression.
(6*13)(0.5)
(6*13)(0.5)=(13*6)(0.5)
by commutative property of multiplication
13(6*0.5)
by associative property of multiplication
13(6*0.5)=13*3=39
500
Write an expression equivalent to
-3(6-11c)
Simplify that expression.
-3(6-11c)=
-3*6-(-3)*11c=
-18--11c=
-18+11c
500
Simplify.
6-2(4x+2x)-2+3(x-7)
6-2(4x+2x)-2+3(x-7)=
6-(6x)-2(x-7)=
-36x+(-2)x+(-2)(-7)=
-36x-2x+14=
-38x+14
500
Solve.
8x+2x(3)=9-2
8x+2x(3)=9-2
8x+2*3*x=7
8x+6x=7
14x=7
(14x)/14=7/14
x=1/2
500
Once a week, you either rent a movie for $4 or see a movie in a theater for $9. Let
r
represent the number of movies you rent in a year (52 weeks). Write and simplify an expression in terms of
r
for the total amount you spend on movies during the year.
movies I rent in a year:
r
movies I see in a theater in a year:
52-r
Amount spent:
4*r+9(52-r)
4r+9*52-9*r
4r+468-9r
-5r+468