Distributive Property
(6.EE.3)
(6.EE.3)
Rewrite using distributive property.
5(7 + 4)
35 + 20
Combine like terms to write an equivalent expression.
4x + 8x2 + x + 6 – 3
8x2 + 5x + 3
Evaluate 7z + 9 when z = 11. Show your work.
7(11) + 9
77 + 9
= 86
Solve. Make sure to show the process, not just an answer.
13.7 = .57 + x
13.7 = .57 + x
-.57 -.57
13.13 = x
Identify the independent and dependent variables.
y = 17 - x
Independent: x
Dependent: y
Rewrite using distributive property
(8 - 3)9
72 - 27
Combine like terms to write an equivalent expression.
7 + 4x2 + 6x2 + x + x2 – 4
Evaluate 8x + x - 3 when x = 4. Show your work.
8(4) + 4 - 3
32 + 4 - 3
36 - 3
= 33
A store receives 200 shirts in 25 boxes. Each box contains the same number of shirts, x.
The equation 25x = 200 represents the situation. Solve the equation to find out how many shirts were in each box.
25x = 200
÷25 ÷25
x = 8
Each box had 8 shirts.
Identify the independent and dependent variables.
12n = r
Independent: n
Dependent: r
Rewrite using distributive property
4(x + 2)
4x + 8
Simplify to write an equivalent expression.
9(2 + 5x) - 10x + 2
9(2 + 5x) - 10x + 2
18 + 45x - 10x + 2
= 20 + 35x
or 35x + 20
Which value in the set {10, 11, 12, 13} is a solution of the equation 19 = 8 + y? Show your work.
11
19 = 8 + y
19 = 8 + 11
19 = 19
Francisca has 54 paperbacks on her bookcase. This is 45% of the books on the bookcase. The equation 0.45b = 54 represents the situation.
Solve the equation to find how many total books, b, Francisca has on her bookshelf.
0.45b = 54
÷ .45 ÷ .45
b = 120
Francisca has 120 books on her bookshelf.
Fill in the rest of the table using the equation
y = 75 - x
x 75 - x y
0
1
2
3
x 75 - x y
0 75 - 0 75
1 75 - 1 74
2 75 - 2 73
3 75 - 3 72
Rewrite using distributive property
(7 - 3m)12
84 - 36m
Which pair of expressions are equivalent?
A) 10g - 2 and 8g
B) c + c + a + a + a and 2c + 3a
C) 3q ÷ 5 and 5q ÷ 3
B
c + c = 2c
a + a + a = 3a
Which value in the set {5, 6, 7, 8, 9} is a solution of the equation 34 – f = 28? Show your work.
6
34 - f = 28
34 - 6 = 28
28 = 28
Mae buys some milk and bread at the grocery store. She paid $9 total. If Mae paid $3 for the milk, how much did she pay for the bread, b. Write and solve an equation.
b + 3 = 9
- 3 - 3
b = 6
Mae paid $6 for the bread.
Fill in the table below and graph the situation using the equation w = 15 + h
h 15 + h w
0
1
2
3
h 15 + h w
0 15 + 0 15
1 15 + 1 16
2 15 + 2 17
3 15 + 3 18
Are these expressions equivalent? Show your work.
2(6x + 2) and 4(3x + 1)
Yes
2(6x + 2) = 12x + 4
4(3x + 1) = 12x + 4
The cost for a taxi ride is $4.00 for the first mile and $3.00 for each additional mile. Rewrite the expression 4 + 3(m - 1) for the cost of the taxi ride in dollars as a sum of two terms, where m represents the miles traveled. Show your work.
4 + 3(m - 1)
4 + 3m - 3
= 1 + 3m
or 3m + 1
Which value in the set {7, 8, 49, 52, 63} is a solution of the equation 7g = 56? Show your work.
8
7g = 56
7(8) = 56
56 = 56
Baxter's Hardware has some followers, f, on their social media account on Friday. Over the weekend, the account loses 5 followers. On Monday morning, Baxter's Hardware has 42 overall followers. Write and solve an equation to find how many followers Baxter’s Hardware had on Friday.
f - 5 = 42
+ 5 + 5
f = 47
Baxter's started with 47 followers.
Fill in the table below and graph the situation using the equation p = 15b
b 15b p
0
1
2
3
b 15b p
0 15(0) 0
1 15(1) 15
2 15(2) 30
3 15(3) 45