Class 3 Handout - Brookdale CC



Class 3 Handout

Review Activity for Chapter 4

Sections 4.1

1. A can be used to indicate the number of equal parts of a

whole.

2. A fraction is less than 1.

3. What common factor do the numerator and denominator of the following

fractions have (other than 1)?

a) [pic][pic] [pic] c) [pic]

b) [pic] d) [pic]

| | | | | |

4. Why can’t we say that [pic] of the figure is shaded?

5. What concept does this statement illustrate?

[pic]

6. What does it mean for a fraction to be in lowest terms?

7. Simplify each to lowest terms:

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

8. Write each fraction as an equivalent fraction with the indicated denominator:

a) [pic], denominator of 40 c) [pic], denominator of 60

b) [pic], denominator of 32 d) [pic], denominator of 14x

Section 4.2

9. Multiply without a calculator. Write all answers in lowest terms.

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

10. a) Write the formula for the area of any triangle.

b) Use the formula from part a to find the area of the following right triangle. Be sure to include units.

5 Feet

7 Feet

11. A tennis ball is dropped from a height of 54 inches. Each time it hits the ground,

it rebounds one-third of the previous height. Find the height after each of the first

3 bounces.

Height after 1st bounce:

Height after 2nd bounce:

Height after 3rd bounce:

Section 4.3

12. Two numbers are called if their product is 1.

13. Explain how to divide two fractions.

14. Find each quotient without a calculator. Write all answers in lowest terms.

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

15. A recipe calls for [pic] cup of flour, and the only measuring container you have holds [pic]cup. How many [pic] cups of flour would you need to add to follow the recipe?

a) Define your variable: x =

b) Set up your equation:

c) Solve your equation:

d) Answer: You need [pic]cups.

16. A set of forestry maps divides 6,284 acres of an old-growth forest into [pic]-acre sections. How many sections do the maps contain?

a) Define your variable: x =

b) Set up your equation:

c) Solve your equation:

d) Answer: There are sections.

Section 4.4

17. A number is the sum of a whole number and a proper fraction.

18. Write down the signed number that could be used to describe the following situation:

A temperature of five and one-half degrees below zero.

19. Simplify each expression without a calculator and leave all answers in lowest terms.

a) [pic] e) [pic]

b) [pic] f) [pic]

c) [pic] g) [pic]

d) [pic] h) [pic]

Section 4.5

20. List the first eight multiples of 9 and the first eight multiples of 12. What is the LCM of 9 and 12?

21. The denominators of two fractions involved in a subtraction problem have the prime-factored forms [pic] and [pic]. What is the LCD for the fractions?

22. For each problem:

i) Find the Least Common Denominator.

ii) Rewrite the fractions with the new denominator, if necessary.

iii) Show the complete solution with all the work.

iv) Reduce the final answer to lowest terms, if necessary.

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

23. A truck can safely carry a one-ton load. Should it be used to deliver one-half ton of sand, one-third ton of gravel, and one-fifth ton of cement in one trip to a job site?

24. What is the difference in strength between a [pic]hp and a [pic]hp garage door opener?

Section 4.6

25. Find each sum or difference without a calculator.

For each problem, find the LCD, perform the indicated operation, and leave answers as mixed numbers in lowest terms.

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

26. To make some draperies, Liz needs [pic] yards of material for the den and [pic] yards for the living room. If the material only comes in 21-yard bolts, how much will be left over after both sets of draperies are completed?

27. Ming Lin needs [pic]inches from a 100 inch spool of wire in order to be able to repair part of a bad wire. How much wire is left on the spool?

Section 4.7

28. Evaluate each expression, using the following steps:

i) List all the operations in each problem as they appear from left to right.

ii) State which operation must be performed first.

iii) Evaluate. Show all steps. Reduce answer to lowest terms, if necessary.

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

29. Evaluate: [pic] for [pic], [pic], [pic]

Section 4.8

30. Solve each equation:

a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

Additional Application Problems

For each problem, define a variable, set up an equation and solve it. Then write your

answer in a complete sentence.

1. When the shutter of a camera stays open longer than [pic] second, any movement of the camera will probably blur the picture. With this in mind, if a photographer is taking a picture of a fast-moving object, should she select a shutter speed of [pic] or [pic]?

2. The surface of the Earth covers an area of approximately 196,800,000 square miles. About [pic] of that area is covered by water. Find the number of square miles of the surface covered by water.

3. Each lap around a stadium track is [pic]mile. How many laps would a runner have to complete to get a 26-mile workout?

4. A cement mixer can carry [pic] cubic yards of concrete. If it makes 8 trips to a job site with a full load each time, how much concrete will be delivered to the site?

5. An amusement park added a new section to a water slide to create a slide [pic] feet long. If the addition is [pic]feet long, how long was the original slide, before the addition was added?

6. A sandwich shop sells a [pic]pound club sandwich, made up of turkey meat and ham. The owner buys the turkey in [pic]pound packages and the ham in [pic]pound packages. If he mixes one package of each type of meat together, how many [pic]pound club sandwiches can he make from the mixture?

7. During a checkup, a pediatrician found that only four-fifths of a child’s baby teeth had emerged. The mother counted 16 teeth in the child’s mouth. How many baby teeth will the child eventually have?

8. Objects on the moon weigh only one-sixth as much as on Earth. How much will an astronaut weigh on the moon if he weighs 180 pounds on Earth?

Class 3 Handout Answer Key

1. Fraction

2. Proper

3. a) 2 c) 3

b) 5 d) 7

4. The 5 parts are not the same size.

5. Equivalent fractions.

6. It means that the fraction has been reduced to the point where the numerator

and the denominator do not have any factors in common.

7. a) [pic][pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) 8y

8. a) [pic] c) [pic]

b) [pic] d) [pic]

9. a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

10. a) [pic]

b) [pic]square feet

11. After the first bounce: 18 in.

After the second bounce: 6 in.

After the third bounce: 2 in.

12. Reciprocals

13. Multiply the first fraction by the reciprocal of the second fraction.

14. a) [pic] d) [pic]

b) 1 e) [pic]

c) [pic] f) 40

15. a) x = The number of [pic]cups needed.

b) [pic]x =[pic]

c) x = 6

d)You need 6 of the[pic]cups.

16. a) x = The number of sections the map contains.

b) [pic]= [pic]

c) x = 7855

d) There are 7855 sections.

17. Mixed.

18. [pic]

19. a) [pic] e) [pic]

b) 14 f) [pic]

c) [pic] g) [pic]

d) [pic] h) [pic]

20. 9: 9, 18, 27, 36, 45, 54, 63, 72

12: 12, 24, 36, 48, 60, 72, 84, 96

LCM is 36

21. LCD is 60

22. a) i) 25 d) i) 8

ii) [pic] ii) [pic]

iii) [pic] iii) [pic]

iv) [pic] iv) [pic]

b) i) x e) i) 15

ii) [pic] ii) [pic]

iii) [pic] iii) [pic]

iv) [pic] iv) [pic]

c) i) 12 f) i) 24

ii) [pic] ii)[pic]

iii) [pic] iii) [pic]

iv) [pic] iv) [pic]

23. No, as [pic]ton

24. [pic]hp

25. a) [pic] d) [pic]

b) [pic] e) [pic]

c) [pic] f) [pic]

26. [pic]yard left over

27. [pic]inches left on the spool

28. a) i) multiplication, addition,

exponent

ii) exponent

iii) [pic]

b) i) multiplication, addition,

exponent, multiplication

ii) exponent

iii) -10

c) i) division

ii) division

iii) [pic]

d) i) subtraction, subtraction,

multiplication

ii) multiplication

iii) [pic]

e) i) division, addition

ii) division

iii) -2

f) i) division

ii) division

iii) [pic]

29. [pic]

29. a) x = 28 d) a = 14

b) x = [pic] e) y = 75

c) t = [pic] f) r = [pic]

Additional Application Problems

1. She should use a shutter speed of [pic]as [pic]< [pic], whereas [pic]>[pic].

2. 147,600,000 square miles of the Earth is covered by water.

3. A runner would have to run104 laps.

4. 76 cubic yards of concrete will be delivered.

5. The slide was[pic]feet long.

6. He can make 17 subs.

7. The child will have 20 teeth.

8. The astronauts weighs 30 pounds.

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