5. Perform the following calculations without a calculator. Then use your calculator to verify your result.
a. 45 , 3 + 12 b. 54 , 9 - 2 # 3
c. 12 + 30 , 2 # 3 - 4 d. 26 + 2 # 7 - 12 , 4
6. a. Explain why the result of is 13.
b. Explain why the result of is 6.
7. Evaluate the following and verify on your calculator.
72 , 18 + 42 72 , 8 + 4
4. Use the distributive property to evaluate each expression.
a. 17150 - 22 b. 190 - 725
a. 48 , 14 + 42 b. 8 + 12
6 - 2 e. Which two arithmetic expressions above yield the same answer?
2. Evaluate each expression, and use your calculator to check your answers.
a. 201100 - 22 b. 20 # 100 - 2
c. 20 # 98 d. 100 - 20# 2
e. Which two arithmetic expressions above yield the same answer?
3. Use the order of operations convention to evaluate each expression.
a. 17150 - 22 b. 190 - 725
c. 7 # 25 d. 20 + 7 # 5
1. Evaluate each expression, and use your calculator to check your answers.
a. 7120 + 52 b. 7 # 20 + 5
Exercise numbers appearing in color are answered in the Selected Answers appendix.
c. 120 , 16 + 42 d. 64 , 16 - 22 # 2
e. 116 + 842 , 14 # 3 - 22 f. 16 + 22 # 20 - 12 , 3
g. 39 + 3 # 18 , 2 + 32 h. 100 - 181 - 27 # 32 , 3
8. Evaluate the following. Use a calculator to verify your answers.
a. 15 + 2 # 53 b. 5 # 24 - 33
c. 52 # 23 , 10 - 6 d. 52# 2 - 5 # 23
9. Evaluate each of the following arithmetic expressions by performing the operations in the appropriate order. Use a calculator to check your results.
a. 37 - 2118 - 2 # 52 + 12 b. 35 + 2 # 102
c. 243
36 - 33 d. 175 - 2 #152 , 9
e. 7 # 23 - 9 # 2 + 5 f. 25# 52
g. 23 # 22 h. 62 + 26
i. 1350 , 75 # 5 - 15 # 2 j. 132 - 422
10. The following numbers are written in standard notation. Convert each number to scientific notation.
a. 213,040,000,000 b. 555,140,500,000,000
11. The following numbers are written in scientific notation. Convert each number to standard notation.
a. 4.532 * 1011 b. 4.532 * 107
12. To solve the following problem, change the numbers to scientific notation and then perform the appropriate operations.
The distance that light travels in 1 second is 186,000 miles. How far will light travel in 1 year? (There are approximately 31,500,000 seconds in 1 year.)
13. Evaluate each formula for the given values.
a. for and
b. for and
c. for and
d. , for and
e. A = t1 + t2 + t3
3 ,fort1 = 76,t2 = 83,andt3 = 81 r = 125 v = 25,
m = 200, F = mv2
r
h = 25 l = 100,w = 5,
V = lwh,
a = 25 m = 120
F = ma,
t = 6 r = 35
d = r # t,
Cluster 1 What Have I Learned?
Activities 1.1 and 1.2 gave you an opportunity to develop some problem-solving strategies. Apply the skills you used in this cluster to solve the following problems.
Exercise numbers appearing in color are answered in the Selected Answers appendix.
1. Your last class for the day is over! As you grab a water bottle and settle down to read a chapter of text for tomorrow’s class, you notice a group of students forming a circle outside and beginning to randomly kick an odd-looking ball from person to person. You notice that there are 12 students in the circle and that they are able to keep the object in the air as they kick it. Sometimes they kick it to the person next to them; other times they kick it to someone across the circle.
a. Suppose each student kicks the Hacky-Sack (you’ve discovered the odd-looking ball has a name) exactly once to each of the others in the circle. How many total kicks would that take?
b. One student in the circle invites you and another student to join them for a total of 14. How many kicks would it now take if each student kicks the Hacky-Sack exactly once to each of the others? How do you arrive at your answer?
c. George Polya’s book How to Solve It outlines a four-step process for solving problems.
i. Understand the problem (determine what is involved).
ii. Devise a plan (look for connections to obtain the idea of a solution).
iii. Carry out the plan.
iv. Look back at the completed solution (review and discuss it).
Describe how your procedures in parts a and b correspond with Polya’s suggestions.
2. You are assigned to read War and Peace for your literature class. The edition you have contains 1232 pages. You time yourself and estimate that you can read 12 pages in 1 hour. You have 5 days before your exam on this book. Will you be able to finish reading it before the exam?
Cluster 1 How Can I Practice?
1. Describe the relationship shared by consecutive numbers in the following sequences.
a.
b.
c.
2. Evaluate each of the following arithmetic expressions by performing the operations in the appro-priate order. Use your calculator to check your results.
1,3,7,15,31,63,Á 1,2,4,8,Á
1,4,7,10,Á
Exercise numbers appearing in color are answered in the Selected Answers appendix.
a. 416 + 32 - 9 # 2 b. 5# 9 , 3 - 3 # 4 , 6
c. 2 + 3 # 43 d. 256
28 + 62
e. 7 - 318 - 2 # 32 + 22 f. 3# 25 + 2 # 52
g. 144 , 124 - 232 h. 36 - 2 # 9
6
i. 9 #5 - 5 # 23 + 5
j. 15# 51 k. 23 # 20
l. 72 + 72 m. 132 - 4 # 022
a. 80 b. 122 3. Write each number in standard notation.
c. 34 d. 26
4. a. Write 214,000,000,000 in scientific notation.
b. Write in standard notation.
5. A newly discovered binary star, Shuart 1, is located 185 light-years from Earth. One light-year is 9,460,000,000,000 kilometers. Express the distance to Shuart 1 in kilometers. Write the answer in scientific notation.
6. The human brain contains about 10,000,000,000 nerve cells. If the average cell contains about 200,000,000,000,000 molecules, determine the number of molecules in the nerve cells of the human brain.
7. Identify the arithmetic property expressed by each numerical statement.
a.
b.
8. Determine if each of the following numerical statements is true or false. In each case, justify your answer.
a.
b.
c.
9. Evaluate each formula for the given values.
a. for and
b. for
c. A = a + b for and a = 65 b = 85 2 ,
s = 7 A = s2,
w = 3 l = 5
A = lw, 1 0 = 1
25 - 10 - 4 = 25 - 110 - 42 7120 + 22 = 7 #22
15 # 9 = 15110 - 12 = 15 # 10 - 15 #1 25 # 30 = 30# 25
7.83 * 104
Activity 1.4
Cluster 2 Problem Solving with Fractions and Decimals (Rational Numbers)
Problem-solving situations frequently require the use of fractions and decimals in their solu-tions. If you need some help working with fractions and decimals, Appendixes A and B con-tain detailed explanations, examples, and practice exercises with worked-out solutions.
As part of the final exam in your culinary arts class, you are asked the following questions.
Remember to reduce each fraction and to use mixed numbers when appropriate. Good luck!
2. List the ingredients needed for the crab recipe if 18 people attend the party.
small (6 oz.) cans crabmeat eggs, hard-boiled and mashed
1. Determine the ingredients for one-half of the crab recipe. Fill in the blanks below.
small (6 oz.) cans crabmeat egg, hard-boiled and mashed cup(s) mayonnaise
tbsp. chopped onion tbsp. plain yogurt