See the attachment

DATA IN OUR LIFE

You probably use properties of operations every day without even giving them a thought. You may have noticed that 3 x 4 and 4 x 3 are both 12. That’s an example of the commutative property of multiplication. The ideas are probably familiar – you just need to brush up on the vocabulary. The associative and commutative properties hold for both addition and multiplication. Associative property of addition – when three or more numbers are added, the way the numbers are grouped does not change the sum.

(2 + 3) + 4 = 2 + (3 + 4) 5 + 4 = 2 + 7 9=9

Associative property of multiplication – when three or more numbers are multiplied, the way the numbers are grouped does not change the product.

(2 x 3) x 4 = 2 x (3 x 4) 6 x 4 = 2 x 12 24 = 24

Commutative property of addition – When two or more numbers are added, the order of the numbers does not change the sum.

2 + 5 = 5 + 2 7 = 7

Commutative property of multiplication – When two or more numbers are multiplied, the order of the numbers does not change the product.

2 x 5 = 5 x 2 10 = 10

Distributive property of multiplication over addition The product of a number and a sum may be expressed as the sum of two products

3 x (1 + 4) = (3 x 1) + (3 x 4) 3 x 5 = 3 + 12 15 = 15

To summarize: There are three properties that you need to know well:

1) Commutative Property: A + B = B + A ex: 15 + 10 = 10 + 15

A * B = B * A ex: 5 x 7 = 7 x 5

2) Associative Property: A + ( B + C) = (A + B) + C example: 5 + (6 + 7) = ( 5 + 6) + 7

A ( B X C) = (A x B) x C example: 5 ( 6 x 7) = ( 5 x 6) x 7

3) Distributive Property: A ( B + C) = AB + AC example: 5 (3 + 6) = 5 x 3 + 5 x 6

A (B – C) = AB – AC example: 6 ( 9 – 7) = 6 x 9 – 6 x 7

Name: __________________________________________________ Date:______________

Which of the following statements illustrate the distributive, associative, and the commutative property?

1) 5 + 9 = 9 + 5

2) 17 x 15 = 15 x 17

3) 19 + 10 = 10 + 19

4) 7 x 92 = 92 x 7

5) 5 ( 8 + 9) = 5 x 8 + 5 x 9

6) 9 ( 15 – 8) = 9 x 15 – 9 x 8

7) 9 x (5 x 7) = (9 x 5) x 7

8) Explain whether or not the commutative property holds for subtraction operation. Give an example to justify your answer.

9) Explain whether or not the commutative property holds for the division operation. Give example to justify your answer.

10) Explain whether or not the associative property holds for the division operation. Give an example to justify your answer.

11) Marie states that 500 (10 ÷ 2) = (500 ÷ 10) x (500 ÷ 2). Do you agree or disagree with Marie’s conjecture? Explain your answer.

12) Provide three examples illustrating the application of the commutative property.

13) Provide three examples illustrating the application of the associative property.

14) Provide three examples illustrating the application of the distributive property.

Name:__________________________________

Sample application problems with signed numbers

1. In one month, Oprah gained 10 pounds. The next month she lost 8 pounds. She then gained 3 pounds the third month. Find Oprah’s net gain or loss.

2. In the morning, you deposited $645.00 into your checking account. The next day, you wrote a check in the amount of $665.00 to Berkeley College which was cashed. What number describes your checking account net change?

3. The NY Jets completed a pass for a gain of 32 yards. After the play was over, a flag was thrown, and a 15-yard penalty was called against the team. What was the net result of the play?

4. Complete the table below

5. A bicycle manufacturer records a profit of $33,300 in April, followed by a loss of $29,250 in May, and a profit of $6375 in June. What is the net effect of these three results?

6. Jennifer got a monthly cable bill for a base rate of $89.00, an additional $9.99 for a package of movie channels, a charge of $11.25 for taxes, and a credit of $11.20 to make up for a billing error the previous month. How much was the cable bill?

7. Roger predicts that the temperature will drop 2 degrees each hour for the next 9 hours. If the temperature is 12 degrees before it starts falling, what is the temperature after the final drop?

8. If F = (9/5) C + 32, find F when C = -485 degrees.

9. A checking account had a beginning balance of $622.00 A deposit was made in the amount of $657. Every month for 16 months, $52 was withdrawn. How much money was left in the account at the end of the 16 months?

10. In a few sentences, explain the process for adding, subtracting, multiplying and dividing signed numbers.

Name:_____________________________ Date:__________________

Perform the indicated operations:

1) -5 ( 9 – 12) =

2) -12 ( -17 + 13) =

3) 17 ( 12 – 19) =

4) 25( -12 + -13) =

5) (0)(398)(140) + (19)(-2) =

6) (-6)(2) + (-4)(-3) =

7) (-7)(-3) + (9) (-3) =

8) (12)(-5) – (9) (6) =

9) (12)(7) – (6)(19) =

10) (-2)(-3)(-4) - (3)(2)(4) =

11) -3 +16 – 27 =

12) 19 – (-9) + 12 =

13) -25 – (-12) + 17 =

14) 125 ÷ - 5 =

15) -300 ÷ - 30 =

16) 18 ÷ - 9 x -3 =

17) (-2) 3 =

18) (-2)4 =

19) (-1) 100 =

20) (-1) 249 =

Name _______________

Find each sum or difference by combining like terms.

1. (4a - 5) + (3a + 6) 2. (3p2 - 2p + 3) - (p2 - 7p + 7)

3. (7x2 - 8) + (3x2 + 1) 4. (x2 + y2) - (-x2 + y2)

5. 5a2 + 3a2x - 7a3 6. 5x2 - x - 4

(+) 2a2 - 8a2x + 4 (-) 3x2 + 8x - 7

7. 2x + 6y - 3z + 5 8. 11m2n2 + 2mn - 11

4x - 8y + 6z - 1 (-) 5m2n2 - 6mn + 17

(+) x - 3y + 6

9. (5x2 - x - 7) + (2x2 + 3x + 4) 10. (5a + 9b) - (4b + 2a)

11. (5x + 3z) + 9z 12. 6p - (8q + 5p)

13. (5a2x + 3ax2 - 5x) + (2a2x - 5ax2 + 7x) 14. (x3 - 3x2y + 4xy2 + y3) - (7x3 -9x2y + xy2 + y3)

15. (d2 - d + 5) - (-d2 + d + 5)

Find the measure of the third side of each triangle. P is the measure of the perimeter.

16. P = 3x + 3y 17. P = 7x + 2y

3x - 5y

2x + y

x + y

x + y

NAME:___________________________ Date:_______________

1. Simplify each expression in the table below:

1. Evaluate the following algebraic expressions:

a) 11D +13Q + 7N when D = $1.00, Q = $0.25 and N = $0.05

b) 18H + 15N + 12P when H = $0.50, N = $0.05 and P = $0.01

c) 5X -10Y + 5 when X = 2 and Y = 3

d) -4W + 6Z – 9 when W = 3, and Z = 2

e) 3C -7D + 10 when C = -7 and D = 5

f) -12 V – 13X -27 when V = -4 and X = 2

3. Your French friend is visiting New York. He is watching the news and he sees that it will be 75 Degrees F tomorrow. This doesn’t mean anything to him so you perform a quick calculation to determine the temperature in C. What is that temperature?

C = (5/9) (F – 32)

3. You have visited 5 places in the world and recorded the temperatures at each place. These five places are shown on the world map that is provided for you. At each location you have measured the temperature and recorded it in the table below.

a) Take a guess on the country where the measurement was taken.(It’s important to know geography too!)

b) Convert the measurement into Fahrenheit based on the formula

F = C + 32