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.

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. [tex]8 \times 34 \implies (8\times 4)+ (8 \times 30)=32+240=272[/tex]

2. [tex]5 \times 47 = (5 \times 7)+ (5 \times 40)=35+200=235[/tex]

3. [tex]12 \times 43= (12 \times 3)+(12 \times 40)=36+480=516[/tex]

4. [tex]8 \times 33=(8 \times 3) + (8 \times 30)=24+240=264[/tex]

5. [tex]6 \times 4.4=60 \times 44=(60 \times 4)+(60 \times 40)=240+2400=2640 \implies 26.40[/tex]

6. [tex]7 \times 2.9= 70 \times 29=(70 \times +9)+(70 \times 20)=630+1400=2030 \implies 20.30[/tex]

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

7. [tex]6(n+4)=6\times n + 6\times 4=6n+24[/tex]

8. [tex]15(2+r)=15 \times 2 + 15 \times r=30+15r[/tex]

9. [tex]8(s+5)=8 \times s + 8 \times 5= 8s+40[/tex]

10. [tex]3(b+8)=3b+24[/tex]

11. [tex]5(6+b)=60+5b[/tex]

12. [tex]9(3+v)=27+9v[/tex]

13. [tex]7(r-7)=7r-49[/tex]

14. [tex]12(4-v)=48-12v[/tex]

15. [tex]11(3-s)=33-3s[/tex]

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

[tex]4(tickets)+4(popcorn)=4(8.50)+4(5.25)=34+21=\$55[/tex]

They spend $55 in total.

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

[tex]12(candy)+12(soda)=12(3.75)+12(4)=45+48=\$93[/tex]

They spent $93 in total.

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

[tex]3(nachos)-3(popcorn)=3(6)-3(5.25)=18-15.75=\$2.25[/tex]

So, the difference between both orders is $2.25.