Based on what you've read, answer the following questions.

1. Use the distributive property to solve the following problems.
a. 8(5 + 25) = ?
b. 12(2 – 5) = ?
c. 3(5 – 12) = ?
d. 4(2 + 1) = ?

2. Find the value of the expression y ÷ (–2) + 5 if y equals –10.

3. Find the value of the expression x ÷ 3 + 10 if x equals 6.

4. Find the value of the expression 2z + 4 – 6 if z equals 12.

5. Find the value of the expression 6m + 4 4 + 11 if m equals 8.

Solve the following word problems.

6. John has been driving at 60 miles an hour for 3 hours. How many miles has he traveled so far? If the total distance to his destination is 240 miles, how much farther must John drive?

7. A cellular phone company bills customers $24.95 per month plus $0.20 a minute for each minute of phone time used. These charges can be expressed in a formula: B = $24.95 + ($0.20 M). In this formula, B stands for the total amount of the bill and M stands for the number of minutes used. This month, Carlos used 23 minutes of phone time. What will his total cellular phone bill be?

1) a:240

  b:-36

  c:-21

  d:12

2) 10

3) 12

4) 22

5) 103

Step-by-step explanation:

1.

a.  

8(5 + 25) = ?Multiply the 8 times each of the numbers inside the parentheses separately.

8(5) + 8(25) = ?  

40 + 200 = ?Multiply 8 times 5 (8 × 5 = 40). Multiply 8 times 25 (8 × 25 = 200). Add 40 and 200. 240

40 + 200 = 240  

b.  

12(2 − 5) = ?Multiply the 12 times each of the numbers inside parentheses separately.

12(2) − 12(5) = ?  

24 − 60 = ?Multiply 12 times 2 (12 × 2 = 24). Multiply 12 times 5 (12 × 5 = 60). Subtract 60 from 24. −36

24 − 60 = −36  

c.  

3(5 − 12) = ?Multiply the 3 times each of the numbers inside parentheses separately

3(5) − 3(12) = ?  

15 − 36 = ?Multiply 3 times 5 (3 × 5 = 15). Multiply 3 times 12 (3 × 12 = 36). Subtract 36 from 15 (15 − 36 = −21). −21

15 − 36 = −21  

d.  

4 (2 + 1) = ?Multiply the 4 times each of the numbers inside parentheses separately.

4(2) + 4(1) = ?  

8 + 4 = ?Multiply 4 times 2 (4 × 2 = 8). Multiply 4 times 1 (4 × 1 = 4). Add 8 and 4 (8 + 4 = 12). 12

8 + 4 = 12  

2.

y ÷ (−2) + 5 = ?Substitute −10 for y in the equation and solve.

−10 ÷ (−2) + 5 = ?  

−10 ÷ (−2) + 5 = ?Perform the division operation first (−10 ÷ (−2) = 5).

5 + 5 = ?  

5 + 5 = 10Add (5 + 5 = 10). 10

3.

x ÷ 3 + 10 = ?Substitute 6 for x in the equation and solve.

6 ÷ 3 + 10 = ?  

6 ÷ 3 + 10 = ?Perform the division operation first (6 ÷ 3 = 2).

2 + 10 = ?  

2 + 10 = 12Add (2 + 10 = 12). 12

4.

2z + 4 − 6 = ?Substitute 12 for z in the equation and solve.

2(12) + 4 − 6 = ?  

2(12) + 4 − 6 = ?Perform the multiplication operation first (2 × 12 = 24).

24 + 4 − 6 = ?  

24 + 4 − 6 = ?Add and subtract in order from left to right (24 + 4 = 28; 28 − 6 = 22). 22

28 − 6 = ?  

28 − 6 = 22  

5.

6m + 4 ÷ 4 + 11 = ?Substitute 8 for m in the equation and solve.

6(8) + 4 ÷ 4 + 11 = ?  

6(8) + 4 ÷ 4 + 11 = ?Perform the multiplication and division operations in order from left to right. Multiply 6 times 8 (6 × 8 = 48).

48 + 4 ÷ 4 + 11 = ?  

48 + 4 ÷ 4 + 11 = ?Divide (4 ÷ 4 = 1).

48 + 1 + 11 = ?  

48 + 1 + 11 = ?Add in order from left to right (48 + 1 = 49; 49 + 11 = 60).  

49 + 11 = ?  

49 + 11 = 60 60

Solutions to Word Problems

6.

D = RTSubstitute the values into the distance formula and solve. John drove at a rate of 60 miles per hour, so the value of R is 60. He drove for a total of 3 hours, so the value of T is 3.

D = 60 • 3  

D= 60 • 3Multiply (60 × 3 = 180). The value of D is 180, so John has traveled 180 miles so far.

D = 180  

240 − 180 = 60Now, subtract 180 miles from 240 miles to find out how much farther John must drive to reach his destination. John will have to drive 60 more miles.

7.

B = $24.95 + ($0.20 × M)Carlos used 23 minutes of phone time this month, so substitute 23 for M in the formula and solve.

B = $24.95 + ($0.20 × 23)  

B = $24.95 + ($0.20 × 23)Perform the operation in parentheses ($0.20 × 23 = $4.60).

B = $24.95 + $4.60  

B = $24.95 + $4.60Perform the addition ($24.95 + $4.60 = $29.55).  

B = $29.55 Carlos’ cellular phone bill for the month is $29.55.

Step-by-step explanation:

straight from pennfoster