Question

Lesson 6 Homework Practice

The Distributive Property
Find each product mentally. Show the steps you used.
1. 8 × 34 2. 5 × 47 3. 12 × 4 3
−
4
4. 8 × 3 3
−
4
5. 6 × 4.4 6. 7 × 2.9
Use the Distributive Property to rewrite each algebraic expression.
7. 6(n + 4) 8. 15(2 + r) 9. 8(s + 5)
10. 3(b + 8) 11. 5(6 + b) 12. 9(3 + v)
13. 7(r - 7) 14. 12(4 - v) 15. 11(3 - s)
16. MOVIES Use the table that shows the prices
of tickets and various food items at the
movie theater.
a. Four friends each bought a ticket and a
bag of popcorn. How much total money did
they spend?
b. How much money will the movie theater
make if a birthday party of 12 kids each
buys a box of candy and a soda but does not
go see a movie?
c. How much more money will a person spend who buys three orders of
nachos than a person who buys three bags of popcorn?
Item Price
Ticket $8.50
Popcorn $5.25
Soda $4.00
Candy $3.75
Nachos $6.

Answer 1

This detailed answer provides step-by-step solutions to the multiplication problems and demonstrates how to use the Distributive Property to rewrite algebraic expressions. It also calculates the total money spent by four friends at the movie theater, the total revenue from a birthday party buying candy and soda, and the price difference between nachos and popcorn.

Step-by-step explanation:

1. 8 × 34 = 272
2. 5 × 47 = 235
3. 12 × 4 3 - 4 = 144 - 16 = 128
4. 8 × 3 3 - 4 = 24 - 16 = 8
5. 6 × 4.4 = 26.4
6. 7 × 2.9 = 20.3
7. 6(n + 4) = 6n + 24
8. 15(2 + r) = 30 + 15r
9. 8(s + 5) = 8s + 40
10. 3(b + 8) = 3b + 24
11. 5(6 + b) = 30 + 5b
12. 9(3 + v) = 27 + 9v
13. 7(r - 7) = 7r - 49
14. 12(4 - v) = 48 - 12v
15. 11(3 - s) = 33 - 11s

a. Four friends spent a total of $13.75 ($8.50 for tickets + $5.25 for popcorn).

b. The movie theater would make $60 ($3.75 for candy x 12 kids) if the birthday party buys only candy and soda.

c. A person would spend $6.75 more if they buy three orders of nachos instead of three bags of popcorn.

Answer 2

Products: Each product can be mentally solved, we need to multiply each factor by the units digit and then add it to the product with the tenths, as follows

1.
`8 * 34 \implies (8* 4)+ (8 * 30)=32+240=272`

2.
`5 * 47 = (5 * 7)+ (5 * 40)=35+200=235`

3.
`12 * 43= (12 * 3)+(12 * 40)=36+480=516`

4.
`8 * 33=(8 * 3) + (8 * 30)=24+240=264`

5.
`6 * 4.4=60 * 44=(60 * 4)+(60 * 40)=240+2400=2640 \implies 26.40`

6.
`7 * 2.9= 70 * 29=(70 * +9)+(70 * 20)=630+1400=2030 \implies 20.30`

Distributive property: Remember, distributive property is about "distributing" the outside factor with each term in side the parenthesis, as follows

7.
`6(n+4)=6* n + 6* 4=6n+24`

8.
`15(2+r)=15 * 2 + 15 * r=30+15r`

9.
`8(s+5)=8 * s + 8 * 5= 8s+40`

10.
`3(b+8)=3b+24`

11.
`5(6+b)=60+5b`

12.
`9(3+v)=27+9v`

13.
`7(r-7)=7r-49`

14.
`12(4-v)=48-12v`

15.
`11(3-s)=33-3s`

The given table shows the prices. Ticket $8.50, Popcorn $5.25, Soda $4.00, Candy $3.75 and Nachos $6.

a. Each of four bought a tickets and a bag of popcorn, the money spent is

`4(tickets)+4(popcorn)=4(8.50)+4(5.25)=34+21=\$55`

They spend $55 in total.

b. 12 kids buy a box of candy and a soda.

`12(candy)+12(soda)=12(3.75)+12(4)=45+48=\$93`

They spent $93 in total.

c. The difference between three orders of nachos and three bags of popcorn.

`3(nachos)-3(popcorn)=3(6)-3(5.25)=18-15.75=\$2.25`

So, the difference between both orders is $2.25.