Properties
Solving for a Variable
Simplifying Expressions
Word Problems
Miscellaneous
100
Which property is represented?
8(3+5)=8×3+8×5
distributive property
100
4n+6n=30+10
n = 4
100
(4m+6k)+3k
4m + 9k
100
In one week, Jess ran 4 times as many laps of the track as Tyson. Jess ran 24 laps.
Write an equation to represent this:
4t = 24
100
Does this demonstrate the preservation of equality (are these two equivalent?)
5(x+3) and 5x + 3
No. Using the distributive property, the first expression is simplified as: 5x + 15.
200
Which property is represented?
21+14=14+21
commutative property of addition
200
25=5n+10
n = 3
200
5t + 7t +6w - 2w - 3t + p
9t +4w + p
200
In one week, Jess ran 4 times as many laps of the track as Tyson. Jess ran 24 laps. Use your equation to solve how many laps Tyson ran:
4t = 24
t = 6 laps.
Tyson ran 6 laps.
200
Does this demonstrate the preservation of equality? In other words, are these two expressions equivalent?
6(2m+5) and 12m+30
Yes!
300
Which property is represented?
(4×9)×2=4×(9×2)
associative property of multiplication
300
n ÷ 6 = 9
n = 54
300
n = 32
300
35 students went on a field trip. Three small buses were filled, and 5 students travelled in cars. How many students were in each bus?
3b + 5 = 35
b = 10
There were 10 students on each bus
300
7. One-half of a number is subtracted from 18. The answer is 12. What is the number?
Write an algebraic equation to solve.
n = 12
(18 - n/2 = 12)
18 - 12/2 = 12
400
Which property is represented?
5(7h+9)=35h + 45
distributive property
400
3n−5=16
n = 7
400
4(3r+5)+2(r+6)
= 12r+20+2r+12
= 14r + 32
400
Simplify the following:
2(3d + 4) – 1 = 100 ÷ 4
6d+ 8 -1 = 25
= 6d + 7 = 25
= 6d = 18
d = 3
400
Write an expression that represents the following. Let h represent the yellow hexagon, r represent the blue rhombus, and t represent the red trapezoid:
h + 3r + 2t
500
Which property is represented?
4h(5) x 6h = 4h x 5(6h)
associative property of multiplication
500
n – 32 = 10
n = 19
500
3p+8(p−4)
=3p + 8p - 32
=11p - 32
500
Simplify, then solve for s
7s + 9 + s – 2 = 3 + 4 × 5
8s + 7 = 23
8s = 16
s = 2
500
If h (yellow) is $1.50, r (blue) is $4, and t (red) is $2.5, what would the value of this picture be?
h + 3r + 2t
= ($1.50) + 3($4) + 2($2.50)
= $1.50 + $12 + $5
= $18.50