7-9. Adam earns $36 for every four hours of work.  If he continues to be paid at the same rate: Help (Html5)⇔Help (Java)

a. How long will it take him to earn $144?  Show and explain your reasoning. 

b. How long will it take him to earn $222?  Show and explain your reasoning. 

c. How could you describe his rate for a 40-hour work week?  For a 7-hour day?  Show and explain your reasoning. 

7-10. A college has a 2:3 ratio of men to women in its student body.  Help (Html5)⇔Help (Java)

a. What is the ratio of women to men? b. What is the ratio of women to total students? c. What percent of the college is men? d. What fraction of the college is women? 

7-11. For each of the following multiplication problems, first estimate the product.  Then check your estimation by multiplying.  Help (Html5)⇔Help (Java)

a.

b.

c.

e.

7-12. Kip and Jordan are brothers.  Their dad measures them once a year by drawing a line on a doorframe in their house.  Help (Html5)⇔Help (Java)

a. Kip grew from 42  inches to 48  inches.  How much did he grow last year?

b. Jordan was 40  inches and grew 5  inches.  How tall is he now?

c. Which boy grew more last year?

7-13. Draw a rectangle with an area of 22 square units.  Find the perimeter of the rectangle.  Label the length and width of the rectangle.  Help (Html5)⇔Help (Java)

7-19. Beth and Amy are racing to see who can ride a tricycle the fastest.  Help (Html5)⇔Help (Java)

Time (sec) 5 10 15 20

Distance (ft) 11 22 33 44

a. Graph the data about Beth’s travel that is recorded in the table above.

b. What is Beth’s rate of travel?

c. If Amy travels at a rate of 75 feet per 30 seconds, would the line representing her distance and time be steeper or less steep than the graph of Beth’s rate?  Explain your reasoning. 

7-20. The area of the rectangle below is   square inches. Find the perimeter. Show your work.  Help (Html5)⇔Help (Java)

7-21. Complete the Representations of a Portions web for each of the following portions. Show your work so that a team member could understand your process.  Help (Html5)⇔Help (Java)

a. a.  

b.0.7 

c. 16% 

d. 2.45 

7-22. Simplify the expressions below.  Help (Html5)⇔Help (Java)

a. 4 · 4 + 4(5 − 2) + 7b. 7 − 9 ÷ 9 + 4(4 − 3) − 7c. −12 + 3(7 − 4) + 5d. 3(15 − 2 · 6) − 5

7-23. Calculate each of the following products.  Help (Html5)⇔Help (Java)

b. ·

c. 12% of 32.8

d. (27.4)(0.02)

e. 2 ·

7-30. Which company offers the lowest unit rate per minute?  Show how you decided.  Help (Html5)⇔Help (Java)

Company Price # of minutes

AB & C $19.95 100

Berizon $24.95 150

Cinguling $9.95 60

DWest $14.75 100

7-31. The graph at right shows the cost per pound of strawberries at four different stores.  Help (Html5)⇔Help (Java)

a. At which store are strawberries about $2 per pound?

b. What is the rate of cost of strawberries at store B?

c. Which store has the most expensive strawberries?  How can you tell?

7-32. Find the perimeter and area of each triangle below.  Help (Html5)⇔Help (Java)

a.

b.

7-33. Arrange these numbers from greatest to least.  Help (Html5)⇔Help (Java)

7-34. Compute each sum or difference.  Help (Html5)⇔Help (Java)

a. A.

b.

c.

7-44. Draw rectangles to represent each integer, then divide them into the fractional parts indicated in the problem.  Part (a) is done as an example.  Help (Html5)⇔Help (Java)

a. How many one-thirds are in 3?  That is, what is 3 ÷  ?

b. How many one-fourths are in 5?  That is, what is 5 ÷  ?

c. How many one-sixths are in 3?  That is, what is 3 ÷  ?

d. How many one-fifths are in 6?  That is, what is 6 ÷  ?

7-45. Describe how each of the following multipliers would change the dimensions of a photograph.  Help (Html5)⇔Help (Java)

a.

b.

c.

d.

7-46. On graph paper, draw your own small design.  Use only horizontal and vertical line segments for the sides that lie on the paper’s grid lines.  Then draw an enlargement and reduction as described in parts (a) and (b) below.  Help (Html5)⇔Help (Java)

a. A. Enlarge your design so that the ratio of lengths of sides is  .

b. Reduce your design so that the ratio of the lengths of sides is 1:2.

7-47. Find the area and perimeter of each figure below.  Help (Html5)⇔Help (Java)

b.

c.

7-48. For each of the generic rectangles below:

Write the two numbers that are being multiplied.  (They are the length and width of the rectangle.)

Predict the size of the product before calculating and be ready to explain your thinking.

Copy the rectangle on your paper and use it to multiply the given numbers.

Compare the exact answer with your prediction.  How close did you get?  Help (Html5)⇔Help (Java)

a.

b.

7-52. Simplify each of the following expressions.  Help (Html5)⇔Help (Java)

a.

b.

c.

d.

e.

f.

7-53. Calculate each of the following products.  Help (Html5)⇔Help (Java)

a.

b.

c.

d.

e. What do the products in parts (a) through (d) have in common?

7-54. Find the area of the shape below in at least two ways.  Help (Html5)⇔Help (Java)

7-55. Maia was serving five pizzas at the weekly meeting of the student council.  She

wanted to divide the pizzas into slices that were each   of a whole pizza. Help (Html5)⇔Help (Java)

a. a. How many slices will she have?

b. Represent this problem using a mathematical sentence.  Can you find more than one way to do this?

7-56. Calculate each of the following products without using a calculator.  Help

(Html5)⇔Help (Java)

b.

c. (3.1)(0.02)

d.

e.

 

7-64. Without using a calculator, find the following quotients.  Help (Html5)⇔Help (Java)

a.

b. 8.06 ÷ 2.48

c.

7-65.Find the multiplicate inverse of each of the following numbers.  Refer to the Math Notes box in this lesson for help.  Help (Html5)⇔Help (Java)

a.

b.

c.1.5

d. 0.25

7-66. A Giant One lets you change a decimal division problem into a whole-number division problem.  Copy the example below and complete the other problems in the same way.  Help (Html5)⇔Help (Java)

  Decimal Division Problem Multiply by Giant One Whole Number Division Problem Answer

Example 10

     

     

  8.2 ÷ 0.4    

  0.02 ÷ 0.005      

  10.05 ÷ 0.25      

 

7-67. This problem is a checkpoint for mutliplying fractions and decimals. It will be referred to as Checkpoint 7A.Multiply each pair of fractions or each pair of decimals. Simplify if possible.  Help (Html5)⇔Help (Java)

b.

c.

d.

e.

f. 2.71 · 4.5

g. 0.35 · 0.0007

Check your answers by referring to the Checkpoint 7A materials.     

If you needed help solving these problems correctly, then you need more practice.  Review the Checkpoint 7A materials and try the practice problems.  Also consider getting help outside of class time.  From this point on, you will be expected to solve problems like this one quickly and easily. 

7-68. The graph at right displays gas mileage for a new car.  Help (Html5)⇔Help (Java)

a. Use the graph to predict the number of miles the car could travel with three gallons of gas. 

b. Use the graph to predict the number of miles the car could travel with five gallons of gas. 

7-74. Simplify each of the following expressions by using one of the strategies in the Math Notes box for this lesson.  Help (Html5)⇔Help (Java)

a.

b.

c.

7-75. Jamie has 9 gallons of paint that she needs to pour into containers that hold 0.75 gallon.  How many containers will she need?  Help (Html5)⇔Help (Java)

7-76. John and Dave are building a rectangular pen next to the barn for their goat, Ginny.  They plan to use one 60-foot wall of the barn as part of the pen, so they only need to build the remaining three sides.  They want the width of the pen to be half of the length.  How much fencing will they need to complete Ginny’s pen?  Can you find more than one answer?  Help (Html5)⇔Help (Java)

7-77. Name the coordinates of each point in the form (x, y).  Help (Html5)⇔Help (Java) 

7-78. Assume that each of the shaded tiles in the large rectangle at right has an area of 1 square foot.  Use this information to answer the following questions.  Help (Html5)⇔Help (Java)

a.What is the total area of all of the shaded tiles?

b. What is the total area of the rectangle that is not shaded? 

\

7-86. Recall that inverse operations “undo” each other.  Write the inverse operation for each situation below.  Help (Html5)⇔Help (Java)

a. Add 

b. Subtract 1

c. Divide by 8

d. Multiply by 12

7-87. Draw the table below on your paper and look carefully at the algebra tiles to fill in each of the steps.  Use your own numbers in the trials, again considering fractions, decimals, and zero.  Help (Html5)⇔Help (Java)

Steps Trial 1

Trial 2

Trial 3

Algebra Tile Picture

1.  Pick a number      

2.  Add ____              

3.  Multiply by ____             

              

4.  Subtract ____             

            

5.  Divide by ____            

6.  Subtract the original number

                         

7-88. On graph paper, draw a rectangle with a width of 5 units and a length of 7 units.  Help (Html5)⇔Help (Java)

a.Draw a new rectangle that is an enlarged copy of your original rectangle and has a length of 13 units. 

b.Show how you can calculate the width of your new rectangle. 

7-89. Kate has five sandwiches to share with three of her friends.  If each person gets the same amount of sandwich, how much will each person get?  Help (Html5)⇔Help (Java)

7-90. Find the area and perimeter of each figure below.  Help (Html5)⇔Help (Java)

a.

b.

7-96. On your paper, copy the chart below.  Then complete two trials by reading the algebraic expressions.  Write in the steps.  Help (Html5)⇔Help (Java)

StepsTrial

1Trial

2Variable

Expression  

1.      x

2.      6x

3.     6x + 24

4.      6x + 18

5.      x + 3

6.     3

7-97. Translate each of these situations into a variable expression such as those found in a magic number chart.  Help (Html5)⇔Help (Java)

a. Pick a number and multiply it by 7.

b. Pick a number and divide it by 8.

c. Pick a number and reduce it by 10.

d. Pick a number, add 2, then multiply by 5.

7-98. Complete the web at right to represent 0.33 as a percent, as a fraction, and in words.  Help (Html5)⇔Help (Java)

7-99. Simplify each of the following expressions.  Help (Html5)⇔Help (Java)

a.

b.

c.45 − 2(6 + 4 · 3)

7-100. Simplify each of the following expressions.  Help (Html5)⇔Help (Java)

a.

b.

c.