Homework #4
Complete the ratio:
1) 5/6 = ?/12
2) ? : 4 = 12 : 6
3) 3/4 = ?/60
4) 7/8 = 8/?
5) 5/6 = 43/?
6) 5 : 9 = ? : 81
7) 12 : 14 : 20 = ? : 42 : ?
Write each sentence as a ratio:
8) 2 eggs for each cup of milk.
9) 2 teachers for every 9 students.
10) 30 miles per hour.
11) 1 head for every tail.
12) 3 parts concentrate to 8 parts water to 2 parts sugar.
Word Problems:
13) The ratio of men to women at a meeting is 4 to 7. If there are 16 men at the meeting, how many women at the meeting?
14) Pam's car gets 24 miles per gallon of gas. If she drove 144 miles, how many gallons of gas did she use?
15) A cookie recipe calls for 5 tablespoons of butter and makes 6 cookies. If we have 20 tablespoons of butter, how many cookies can we make. How much butter would it take to make 30 cookies?
16) On a blueprint of the Smith house, each 1/4 inch on the drawing is equivalent to 1 foot. If the drawing shows that the doorways are 7/8 of an inch wide, how wide are they in reality?
17) "Ed's Used Cars" sells 2 convertibles for every 46 sedans. If Ed sold 384 cars all together (convertables and sedans), how many convertibles did he sell?
18) If at a certain office there are 6 clerks for every 2 executives, and there are 200 people total (clerks and executives), how many executives are there?
Averages:
19) Find the average of 3, 5, 4, 2, 1, and 1.
20) Find the average of 45, 23, 54, 103, and 44.
21) Find the average of 65, 66, and 65, and 65.
Word Problems:
22) Dan bought 4 boxes of crackers at the market, and their prices were $4.11, $3. 46, $ 1.99, and $ 2.88. What was the average price per box?
23) The chart below shows the price per gallon of gas in the summer. What is the average price of gas in the summer?
June - $2.45
July - $3.54
August - $ 3.70
24) Paula drove 50 miles per hour for 3 hours and the 40 miles per hour for 2 hours. What was her average speed for the entire trip?
25) Bill calculated that his average test score from the 8 tests of the school year was 84. Then he realized he had accidentally divided by 7 instead of 8. What is his real average test score?
Monday, December 14, 2009
Tuesday, December 8, 2009
Homework #3
Percent Problems:
1) What is 50% of 6?
2) What is 40% of 9?
3) 5 is what percent of 10?
4) 6 is what percent 25?
5) 4 is 25% of what?
6) 3 is 23% of what?
7) What is 45% of 5/8?
8) What is 39% of 5 5/7?
9) 4/5 is what percent of 13/5?
10) 76/4 is what percent of 4/3?
11) 5/6 is 43% of what?
12) 7/34 is 235% of what?
13) What is 4% of 4.5?
14) What is 45.5% of 7.34?
15) 5.3 is what percent of 4.5?
16) 56.664 is what percent of 34.443?
17) 4.3 is 43.33% of what?
18) 5.55 is 109.6% of what?
19) Change 32% into a decimal.
20) Change 4% into a decinal.
21) Change 99.99% into a decimal.
22) Change 145.3% into a decimal.
22) Change 0.32 into a percent.
23) Change 0.03 into a percent.
24) Change 2.23 into a percent
25) Change 1/4 into a percent.
26) Change 4/56 into a percent,.
27) Change 45% into a fraction.
28) Change 3.3% into a fraction.
Word problems:
19) A pair of shoes are marked at $100. If there is a 25% off sale, how much are the shoes?
20) A family at a restaurant get a bill for $55.50, and they decide to leave a 20% tip. How much do they leave altogether?
21) The population of gorillas is 75% of what is was last year. If there are now 200 gorillas, how many were there last year?
22) Joe was making $12.35 per hour, and then got a 3% raise. Now how much does he make per hour?
23) If Edna spent 6 hours per night sleeping, what percent of each 24 hour day is she asleep? What percent of each week?
24) Paul spends 15% of his monthly income on the lottery. If he spends $200 per month on the lottery, what is his monthly income?
25) Computo Inc. laid of 23% of its 2000 employees last week. How many of its employees kept their jobs?
Percent Problems:
1) What is 50% of 6?
2) What is 40% of 9?
3) 5 is what percent of 10?
4) 6 is what percent 25?
5) 4 is 25% of what?
6) 3 is 23% of what?
7) What is 45% of 5/8?
8) What is 39% of 5 5/7?
9) 4/5 is what percent of 13/5?
10) 76/4 is what percent of 4/3?
11) 5/6 is 43% of what?
12) 7/34 is 235% of what?
13) What is 4% of 4.5?
14) What is 45.5% of 7.34?
15) 5.3 is what percent of 4.5?
16) 56.664 is what percent of 34.443?
17) 4.3 is 43.33% of what?
18) 5.55 is 109.6% of what?
19) Change 32% into a decimal.
20) Change 4% into a decinal.
21) Change 99.99% into a decimal.
22) Change 145.3% into a decimal.
22) Change 0.32 into a percent.
23) Change 0.03 into a percent.
24) Change 2.23 into a percent
25) Change 1/4 into a percent.
26) Change 4/56 into a percent,.
27) Change 45% into a fraction.
28) Change 3.3% into a fraction.
Word problems:
19) A pair of shoes are marked at $100. If there is a 25% off sale, how much are the shoes?
20) A family at a restaurant get a bill for $55.50, and they decide to leave a 20% tip. How much do they leave altogether?
21) The population of gorillas is 75% of what is was last year. If there are now 200 gorillas, how many were there last year?
22) Joe was making $12.35 per hour, and then got a 3% raise. Now how much does he make per hour?
23) If Edna spent 6 hours per night sleeping, what percent of each 24 hour day is she asleep? What percent of each week?
24) Paul spends 15% of his monthly income on the lottery. If he spends $200 per month on the lottery, what is his monthly income?
25) Computo Inc. laid of 23% of its 2000 employees last week. How many of its employees kept their jobs?
Wednesday, December 2, 2009
Homework #2
Change the fraction to a decimal:
1) 3/4
2) 5/6
3) 5 3/8
4) 2 2/3
5) 56/7
Change the decimal to a fraction and reduce to lowest terms:
6) 0.6
7) 3.45
8) 0.0012
9) 0.777
10) 44.44
11) 1.5
12) 6.200
Put each list of decimals in order from smallest to largest:
13) 0.001, 0.0101, 0.010
14) 3.13, 3.1301, 3.12999999
Round each decimal to the nearest whole number:
15) 3.001
16) 5.5
17) 0.00332
18) 4.9876123
19) 3.511111
Round to the nearest tenth:
20) 3.0510000000
21) 5.005
22) 6.999
23) 1.09999
24) 5.05
Where should the decimal point be placed in each sum?
25) 3.5 + 3.7 = 72
26) 1.4 + 0.8 + 22
27) 4.835 + 1.217 = 6052
28) 7.42 + 125.931 = 133351
Add the following decimals:
30) 1.789 + 0.219
31) 1.48 + 0.9
32) 3.59 +2
33) 10.7 + 8.935
34) 6.1 + 0.29080 +4
35) 14.004 + 0.9 + 0.21
36) 1.03 + 2.5 + 40.016
37) 5.2 + 0.7999 + 0.0001
Subtract the following decimals:
40) 6.4 - 1.3
41) 1.89 - 0.37
42) 12.35 - 8.05
43) 2.35 - 0.9
44) 5 - 3.81
45) 1 - 0.98765
46) 2.4 - 2.3999
Word Problems
47) At the market, Joe bought 2.3 pounds of tomatoes, 5.4 pounds of garlic, 9.12 pounds of tomatoes, and 4.2 pounds of blueberries. How many pounds of produce did he buy in all?
48) Mary improved her time running a mile on the track from 6.3 minutes to 5.56 minutes. By how much did she improve her time?
49) Biff loaned Joe $32.23 at the market to pay for the produce. Joe paid Biff back $25.00 the next day. How much money did Biff make in the deal?
Add these fractions and decimals. Give your answer in fractions and decimals:
50) 1/2 + 0.5
51) 1/4 + 0.25
52) 5/8 + 0.5
53) 4.9 +3/10
54) 0.3 + 7/10
55) 3.15 + 3 5/6
Multiply each decimal:
56) 0.01 × 0.6
57) 3.1 × 4
58) 0.1 × 0.2
59) 15 × 0.21
58) 0.875 × 8
59) 2.5 × 0.0034
60) 100 × 0.01765
61) 38.71 × 1,000
Divide each fraction:
62) 1.4 ÷ 7
63) 51.2 ÷ 4
64) 2.2 ÷ 0.7
65) 256 ÷ 0.0004
Change the fraction to a decimal:
1) 3/4
2) 5/6
3) 5 3/8
4) 2 2/3
5) 56/7
Change the decimal to a fraction and reduce to lowest terms:
6) 0.6
7) 3.45
8) 0.0012
9) 0.777
10) 44.44
11) 1.5
12) 6.200
Put each list of decimals in order from smallest to largest:
13) 0.001, 0.0101, 0.010
14) 3.13, 3.1301, 3.12999999
Round each decimal to the nearest whole number:
15) 3.001
16) 5.5
17) 0.00332
18) 4.9876123
19) 3.511111
Round to the nearest tenth:
20) 3.0510000000
21) 5.005
22) 6.999
23) 1.09999
24) 5.05
Where should the decimal point be placed in each sum?
25) 3.5 + 3.7 = 72
26) 1.4 + 0.8 + 22
27) 4.835 + 1.217 = 6052
28) 7.42 + 125.931 = 133351
Add the following decimals:
30) 1.789 + 0.219
31) 1.48 + 0.9
32) 3.59 +2
33) 10.7 + 8.935
34) 6.1 + 0.29080 +4
35) 14.004 + 0.9 + 0.21
36) 1.03 + 2.5 + 40.016
37) 5.2 + 0.7999 + 0.0001
Subtract the following decimals:
40) 6.4 - 1.3
41) 1.89 - 0.37
42) 12.35 - 8.05
43) 2.35 - 0.9
44) 5 - 3.81
45) 1 - 0.98765
46) 2.4 - 2.3999
Word Problems
47) At the market, Joe bought 2.3 pounds of tomatoes, 5.4 pounds of garlic, 9.12 pounds of tomatoes, and 4.2 pounds of blueberries. How many pounds of produce did he buy in all?
48) Mary improved her time running a mile on the track from 6.3 minutes to 5.56 minutes. By how much did she improve her time?
49) Biff loaned Joe $32.23 at the market to pay for the produce. Joe paid Biff back $25.00 the next day. How much money did Biff make in the deal?
Add these fractions and decimals. Give your answer in fractions and decimals:
50) 1/2 + 0.5
51) 1/4 + 0.25
52) 5/8 + 0.5
53) 4.9 +3/10
54) 0.3 + 7/10
55) 3.15 + 3 5/6
Multiply each decimal:
56) 0.01 × 0.6
57) 3.1 × 4
58) 0.1 × 0.2
59) 15 × 0.21
58) 0.875 × 8
59) 2.5 × 0.0034
60) 100 × 0.01765
61) 38.71 × 1,000
Divide each fraction:
62) 1.4 ÷ 7
63) 51.2 ÷ 4
64) 2.2 ÷ 0.7
65) 256 ÷ 0.0004
Wednesday, November 25, 2009
Here are some problems to practice before Monday 11/30/09. Feel free to email me with any questions you may have.
Reduce to lowest terms:
1) 6/8
2) 56/70
3) 23/46
Convert each improper fraction to a mixed number:
4) 25/10
5) 14/13
6) 8/4
Convert each mixed number to a improper fraction:
7) 5 ½
8) 21 ¼
Find the answer and reduce to lowest terms:
9) 3/8 + 1/8
10) 2/3 - 5/9
11) 1/13 + 5 ¼
12) 3 5/6 + 6 8/13
13) 1/3 + 6 1/6 - 6 1/2
14) 4/3 × 6/7
15) 1/6 × 4 3/4
16) 13/24 × 1 1/3
17) 3/5 ÷ 4/3
18) 3/7 + 5/6 ÷ 1 13/14 × 5 6/7 - 1/3
Reduce to lowest terms:
1) 6/8
2) 56/70
3) 23/46
Convert each improper fraction to a mixed number:
4) 25/10
5) 14/13
6) 8/4
Convert each mixed number to a improper fraction:
7) 5 ½
8) 21 ¼
Find the answer and reduce to lowest terms:
9) 3/8 + 1/8
10) 2/3 - 5/9
11) 1/13 + 5 ¼
12) 3 5/6 + 6 8/13
13) 1/3 + 6 1/6 - 6 1/2
14) 4/3 × 6/7
15) 1/6 × 4 3/4
16) 13/24 × 1 1/3
17) 3/5 ÷ 4/3
18) 3/7 + 5/6 ÷ 1 13/14 × 5 6/7 - 1/3
19) Joe makes a pizza and invites 6 friends over to eat. He cuts the pizza into 7 equal slices so each person will get one slice. Only 4 slices are eaten, and he decides to split the remaining slices between 2 friends to take home. What fraction of a whole pizza does each friend get to take home?
20) Joe buys 8 1/2 pounds of flour to make a huge pizza. He decides to make a pizza 1/3 of the size he originally planned for. How much flour does he end up using?
Thursday, November 12, 2009
Welcome to the Kaiser Math Review!
Thank you for taking a moment to allow me to introduce myself and this program.
My name is Nathan James and for the past year I have been the principal tutor hired by the SEIU to assist Kaiser employees taking math classes at PCC. The program has worked well, and many of them have been successful in achieving their career goals. Working with these students, I observed that many were starting at a point well behind where they last left off in school. As a result, the math was easy and boring, and their goals seemed very far away. It seemed to me that if they had a chance to review the material before they took the placement exam, perhaps with a little help, they could skip entire terms of math prerequisites.
It is with this in mind that I designed this program. The goal is to reacquaint you to the math you can expect to see on a community college placement test. We'll focus on the subjects you've seen before but probably haven't used in a while so that you can place into a level of math appropriate to your needs and abilities.
This class should differ from other classes you may have taken previously in three noteworthy ways:
1) Class size will be limited to 10 students, assuring plenty of 1 on 1 attention, and a more relaxed environment where you can feel comfortable asking those "easy" questions (you know, that one that everyone else is quietly wondering about).
2) The class will be restricted to Kaiser employees only, so you don't have to worry about that annoying 18-year-old know-it-all in the front row whom you'll surely find later at community college.
3) The course was designed for you! We have the freedom to continually restructure it to suit your needs, to spend more or less time on a certain subject, or skip subjects altogether. Comments, suggestions, and questions are encouraged in person, via email, or even posted on this blog!
For now, please take a moment to try out some of these problems below. This way, when you arrive on Monday the 23rd, you'll know what you want to work on, and we can adjust the class schedule as needed. Good luck, and congratulations on taking a major step towards a new career!
Nathan James
Math Teacher
Sample Pre-algebra Questions:
1. 54 – 6 ÷ 2 + 6 = ?
A. 6
B. 24
C. 27
D. 30
E. 57
2. The lowest temperature on a winter morning was –8°F. Later that same day the temperature reached a high of 24°F. By how many degrees Fahrenheit did the temperature increase?
A. 3°
B. 8°
C. 16°
D. 24°
E. 32°
3. If (3/4 - 2/3) + (1/2 + 1/3) is calculated and the answer reduced to simplest terms, what is the denominator of the resulting fraction?
A. 24
B. 12
C. 6
D. 4
E. 3
4. 1/2 + ( 2/3 ÷ 3/4) - (4/5 × 5/6) = ?
A. 1/16
B. 17/27
C. 13/18
D. 7/9
E. 5/6
5. Mr. Brown went grocery shopping to buy meat for his annual office picnic. He bought 7 ¾ pounds of hamburger, 17.85 pounds of chicken, and 6 ½ pounds of steak. How many pounds of meat did Mr. Brown buy?
A. 32.10
B. 31.31
C. 26.25
D. 22.10
E. 21.10
6. Four students about to purchase concert tickets for $18.50 for each ticket discover that they may purchase a block of 5 tickets for $80.00. How much would each of the 4 save if they can get a fifth person to join them and the 5 people equally divide the price of the 5-ticket block?
A. $ 1.50
B. $ 2.50
C. $ 3.13
D. $10.00
E. $12.50
7. In scientific notation, 20,000 + 3,400,000 = ?
A. 3.42 × 106
B. 3.60 × 106
C. 3.42 × 107
D. 3.60 × 107
E. 3.60 × 1012
8. Saying that 4 < √x < 9 is equivalent to saying what about x ?
A. 0 < x < 5
B. 0 < x < 65
C. 2 < x < 3
D. 4 < x < 9
E. 16 < x < 81
9. What value of x solves the following proportion?
9/6 = x/8
A. 5 1/3
B. 6 ¾
C. 10 ½
D. 11
E. 12
10. If the total cost of x apples is b cents, what is a general formula for the cost, in cents, of y apples?
A. b/xy
B. x/by
C. xy/b
D. by/x
E. bx/y
11. On a math test, 12 students earned an A. This number is exactly 25% of the total number of students in the class. How many students are in the class?
A. 15
B. 16
C. 21
D. 30
E. 48
12. This year, 75% of the graduating class of Harriet Tubman High School had taken at least 8 math courses. Of the remaining class members, 60% had taken 6 or 7 math courses. What percent of the graduating class had taken fewer than 6 math courses?
A. 0%
B. 10%
C. 15%
D. 30%
E. 45%
13. Adam tried to compute the average of his 7 test scores. He mistakenly divided the correct sum of all of his test scores by 6, which yielded 84. What is Adam’s correct average test score?
A. 70
B. 72
C. 84
D. 96
E. 98
14. A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?
A. 73
B. 75
C. 76
D. 77
E. 78
Correct Answers for Sample Numerical Skills/Prealgebra Items
1. E (Operations with Integers)
2. E (Operations with Integers
3. B (Operations with Fractions)
4. C (Operations with Fractions)
5. A (Operations with Decimals)
6. B (Operations with Decimals)
7. A (Exponents)
8. E (Exponents)
9. E (Ratios and Proportions)
10. D (Ratios and Proportions)
11. E (Percentages)
12. B (Percentages)
13. B (Averages)
14. D (Averages)
Thank you for taking a moment to allow me to introduce myself and this program.
My name is Nathan James and for the past year I have been the principal tutor hired by the SEIU to assist Kaiser employees taking math classes at PCC. The program has worked well, and many of them have been successful in achieving their career goals. Working with these students, I observed that many were starting at a point well behind where they last left off in school. As a result, the math was easy and boring, and their goals seemed very far away. It seemed to me that if they had a chance to review the material before they took the placement exam, perhaps with a little help, they could skip entire terms of math prerequisites.
It is with this in mind that I designed this program. The goal is to reacquaint you to the math you can expect to see on a community college placement test. We'll focus on the subjects you've seen before but probably haven't used in a while so that you can place into a level of math appropriate to your needs and abilities.
This class should differ from other classes you may have taken previously in three noteworthy ways:
1) Class size will be limited to 10 students, assuring plenty of 1 on 1 attention, and a more relaxed environment where you can feel comfortable asking those "easy" questions (you know, that one that everyone else is quietly wondering about).
2) The class will be restricted to Kaiser employees only, so you don't have to worry about that annoying 18-year-old know-it-all in the front row whom you'll surely find later at community college.
3) The course was designed for you! We have the freedom to continually restructure it to suit your needs, to spend more or less time on a certain subject, or skip subjects altogether. Comments, suggestions, and questions are encouraged in person, via email, or even posted on this blog!
For now, please take a moment to try out some of these problems below. This way, when you arrive on Monday the 23rd, you'll know what you want to work on, and we can adjust the class schedule as needed. Good luck, and congratulations on taking a major step towards a new career!
Nathan James
Math Teacher
Sample Pre-algebra Questions:
1. 54 – 6 ÷ 2 + 6 = ?
A. 6
B. 24
C. 27
D. 30
E. 57
2. The lowest temperature on a winter morning was –8°F. Later that same day the temperature reached a high of 24°F. By how many degrees Fahrenheit did the temperature increase?
A. 3°
B. 8°
C. 16°
D. 24°
E. 32°
3. If (3/4 - 2/3) + (1/2 + 1/3) is calculated and the answer reduced to simplest terms, what is the denominator of the resulting fraction?
A. 24
B. 12
C. 6
D. 4
E. 3
4. 1/2 + ( 2/3 ÷ 3/4) - (4/5 × 5/6) = ?
A. 1/16
B. 17/27
C. 13/18
D. 7/9
E. 5/6
5. Mr. Brown went grocery shopping to buy meat for his annual office picnic. He bought 7 ¾ pounds of hamburger, 17.85 pounds of chicken, and 6 ½ pounds of steak. How many pounds of meat did Mr. Brown buy?
A. 32.10
B. 31.31
C. 26.25
D. 22.10
E. 21.10
6. Four students about to purchase concert tickets for $18.50 for each ticket discover that they may purchase a block of 5 tickets for $80.00. How much would each of the 4 save if they can get a fifth person to join them and the 5 people equally divide the price of the 5-ticket block?
A. $ 1.50
B. $ 2.50
C. $ 3.13
D. $10.00
E. $12.50
7. In scientific notation, 20,000 + 3,400,000 = ?
A. 3.42 × 106
B. 3.60 × 106
C. 3.42 × 107
D. 3.60 × 107
E. 3.60 × 1012
8. Saying that 4 < √x < 9 is equivalent to saying what about x ?
A. 0 < x < 5
B. 0 < x < 65
C. 2 < x < 3
D. 4 < x < 9
E. 16 < x < 81
9. What value of x solves the following proportion?
9/6 = x/8
A. 5 1/3
B. 6 ¾
C. 10 ½
D. 11
E. 12
10. If the total cost of x apples is b cents, what is a general formula for the cost, in cents, of y apples?
A. b/xy
B. x/by
C. xy/b
D. by/x
E. bx/y
11. On a math test, 12 students earned an A. This number is exactly 25% of the total number of students in the class. How many students are in the class?
A. 15
B. 16
C. 21
D. 30
E. 48
12. This year, 75% of the graduating class of Harriet Tubman High School had taken at least 8 math courses. Of the remaining class members, 60% had taken 6 or 7 math courses. What percent of the graduating class had taken fewer than 6 math courses?
A. 0%
B. 10%
C. 15%
D. 30%
E. 45%
13. Adam tried to compute the average of his 7 test scores. He mistakenly divided the correct sum of all of his test scores by 6, which yielded 84. What is Adam’s correct average test score?
A. 70
B. 72
C. 84
D. 96
E. 98
14. A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?
A. 73
B. 75
C. 76
D. 77
E. 78
Correct Answers for Sample Numerical Skills/Prealgebra Items
1. E (Operations with Integers)
2. E (Operations with Integers
3. B (Operations with Fractions)
4. C (Operations with Fractions)
5. A (Operations with Decimals)
6. B (Operations with Decimals)
7. A (Exponents)
8. E (Exponents)
9. E (Ratios and Proportions)
10. D (Ratios and Proportions)
11. E (Percentages)
12. B (Percentages)
13. B (Averages)
14. D (Averages)
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