Question

Find the value of each expression.

3. 5 + 4 × 5 – 7

4. 8 × (33 + 2) – 11

5. 30 × 4 – 22 × 5

6. 55 ÷ 5 × 23 ÷ 4

7. Tanya purchased 4 hammers for $11.79 each and 7 screwdrivers for $6.65 each. Write an expression for the total cost of the tools. Then find the total cost.

Evaluate each expression if a = 3, b = 23, and c = 6.

8. 2a + 5

9. 2c + 3a

10. c2 + 3a × b

11. Koby took $43 to the movie theater. If he paid for 3 tickets that each cost d dollars, he will have 43 – 3d left. How much does he have left if the tickets cost $9.75 each?

Write each phrase as an algebraic expression.

12. 16 seconds faster than Najib’s time

13. one piece more than twice the number of pieces

14. one third of Danielle’s height

15. six meters less than four times the width

16. Devante made and sold 8 pitchers of lemonade at his lemonade stand. He used the same number of lemons in each pitcher. He had 3 lemons left over. Write an expression to represent the total number of lemons Devante had in all.

17. Helen divided her colored pencils evenly among herself and three friends. Write an expression to represent the number of pencils each person received.

Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.

18. (8 × 2) × 5 = 8 × (2 × 5)

19. 13 + 0 = 13

20. 12 – (5 – 3) = (12 – 5) – 3

21. Niko worked out for 45 minutes, 22 minutes, and 25 minutes last week. Use the Commutative Property to find the total number of minutes he worked out.

Find each product mentally. Show the steps you used.

22. 6 × 52

23. 4 × 7.1

Use the Distributive Property to rewrite each algebraic expression.

24. 5(x + 9)

25. 11(12 + r)

26. 9(v + 2)

27. 7(b + 3.5)
Item
Cost($)
Pants
19.00
Socks
4.95
T-shirt
12.00

28. Mrs. Sosa bought a T-shirt and a pair of socks for each of her 14 grandchildren. The table lists the cost of each item. Use the Distributive Property to find the total amount of money she spent on her grandchildren.

Simplify each expression.

29. 7x + 3x + 4x

30. 5(2x + 4y)

31. 6x + 2y + 9x

Factor each expression.

32. 9x + 36y

33. 12x + 18y

34. The area of Amy’s rectangular swimming pool, in square feet, can be found by using the expression 5(8x + 10y). Use the distributive property to write an equivalent expression for the area of Amy’s swimming pool.

Equivalent Expression: ___________________________________

Use your equivalent expression to find the area of Amy’s swimming pool, in square feet, if x = 2 and y = 3.

Answer 1

Answer:

3. 5+4×5-7

= 9×5-7

= 9×(-2)

= -18

4. 8×(33+2)-11

= 8×35-11

= 280-11

= 269

5. 30×9-22×5

= 270-110

= 160

6. 55÷5×23÷4

= 11×5.74

= 63.25

8. 2a+5

= 2×3+5

= 6+5

=11

9. 2c+3a

= 2×6+3×3

= 12+9

= 21

10. c2+3a×b

= 6×2+3×3×23

= 12+207

= 219

18. (8×2)×5=8×(2×5)

= 16×5=8×10

= 80=80 (prove)

19. 13+0=13

= 13=13 (prove)

20. 12-(5-3)=(12-5)-3

= 12-8=7-3

= 4=4 (prove)

22. 6×52

= 312

23. 4×7.1

= 28.4

24. 5(x+9)

= 5x+45

25. 11(12+r)

= 132+11r

26. 9(v+2)

= 9v+18

27. 7(b+3.5)

= 7b+24.5

29. 7x+3x+4x

= 14x

30. 5(2x+4y)

= 10x+20y

31. 6x+2y+9x

= 15x+2y

32. 9x+36y

= 9(x+4y)

33. 12x+18y

= 3(4x+6y)