Envision Math 6th Grade Textbook Answer Key Topic 2.4 The Distributive Property

The Distributive Property

How can you use the Distributive Property to evaluate expressions?
The Distributive Property states that multiplying a sum (or difference) by a number gives the same result as multiplying each number in the sum
(or difference) by the number and adding (or subtracting) the products.

Guided Practice

Do you know HOW?
In 1 through 4, find each missing number.
Question 1.
8(7 + 23) = 8(7) + 8(☐)
23
Explanation:

Question 2.
4(28) = 4(20) + 4 (☐)
8
Explanation:

Question 3.
8(57) – 8(7) = 8(☐)
50
Explanation:

Question 4.
5(26 – 3) = 5 (☐) – 5(3)
26
Explanation:

Use mental math to evaluate 5 and 6.
Question 5.
6(32) = ☐
192
Explanation:

Question 6.
20(5) – 20(2) = ☐
60
Explanation:

Do you UNDERSTAND?
Question 7.
Why is it easier to evaluate 7 × 60 than to evaluate 7 × 55 + 7 × 5?
See margin.
Explanation:

Question 8.
Tony read 22 pages in the morning and 28 pages in the afternoon for 5 days. Lois read 47 pages each day for 5 days. Explain howto use the Distributive Property to find how many pages each of them read.
See margin.
Explanation:

Independent Practice

Leveled Practice In 9 through 16, find each missing number.
Question 9.
3(28) + (3)2 = ☐ (30)
3
Explanation:

Question 10.
9(23) = 9(☐) + 9(3)
20
Explanation:

Question 11.
6(46) – 6(6) = 6(☐)
40
Explanation:

Question 12.
4(33) = 4(30) + 4(☐)
3
Explanation:

Question 13.
30(22 – 10) = 30(22) – 30(☐)
10
Explanation:

Question 14.
8(99) = 8(100) – 8(☐)
1
Explanation:

Question 15.
20(33 – 5) = 20(☐)
28
Explanation:

= 20(☐) + 20(8)
20
Explanation:

Question 16.
5(42) + 5(5) = 5(☐)
47
Explanation:

= 5(☐) + 5(7)
40
Explanation:

Use the Distributive Property to break apart a number to find the product for 5 × 27.
5 × 27 ← Break 27 apart.

5(20) +5 (7) ← Multiply each addend.
135
5 × 27 = 135

Use the Distributive Property to join numbers together to find 8(32) – 8(2).
8(32) – 8(2)
8(32 — 2) ← Join factors.
8(30) ← Subtract.
240 ← Multiply.
8(32) – 8(2) = 240

Independent Practice

Use the Distributive Property and mental math to evaluate.
Tips: When doing mental math, choose to join or break apart based on which is easier.
Question 17.
7(29)
203
Explanation:

Question 18.
6(21) + 6(31)
312
Explanation:

Question 19.
5(22) + 5(8)
150
Explanation:

Question 20.
8(47)
376
Explanation:

Question 21.
6(41) + 6(9)
300
Explanation:

Question 22.
30(3) + 30(5)
240
Explanation:

Question 23.
3(21) – 3(11)
30
Explanation:

Question 24.
5(25 – 3)
110
Explanation:

Problem Solving

Question 25.
Writing to Explain The 6th graders ordered lunch from the Big Group Menu.They ordered 22 organic chilis and 8 veggie plates.Their order can be expressed as 6(22) + 6(8). Explain what mental math steps you would use to find the total cost of the order.

See margin.

Question 26.
Using the Big Group Menu, write and solve a problem where you can use the Distributive Property.
See margin.

Question 27.
Writing to Explain Jamal said that 9.45 is greater than 9.8 because 45 is greater than 8. Is he correct? Explain.
No; sample answer: 0.8 = 0.80 and 80 > 45.
Explanation:

Question 28.
Hiroko put money in a savings account each week. After 9 weeks, there was $49.50 in the account. If Hiroko put the same amount in each week, how much did she save each week? Answer:$5.50
Explanation:

Question 29.
Think About the Process Which choice shows a problem with common factors that could be used for mental math?
A. 3(45) + 3(5)
B. 4(18) – 7(8)
C. 2(22) + 3(33)
D. 8(39) + 4(40)