Operations with Whole Numbers
Operations with Whole Numbers SKILL #1: ADDITION 1. 731 + 42 + 100 2. 3200 + 800 + 99 + 9 3. 1 + 11 + 1,101 + 2,011 4. 3,005 + 23 + 36,011 5. The sum of 96; 9; 231; 139; 2,007 SKILL #2: SUBTRACTION 1. 2803 – 532 2. 40,317 – 8,234 3. 98,217 – 463 4. 29,003 – 9,269 5. 112,130 - 16,832 6. Subtract 1,148 from 1,355 7. From 21,093 subtract 20,897 8. Subtract 999 from 2,111 9. The difference between 100,923 and 9,031 10. Find the difference between 78,953 and 4,008 11. Tom weighed 136 pounds. At the end of two month of exercising, Tom weighs 128 pounds. How much weight did Tom lose? 12. Lakeside High School prints 15,000 raffle tickets. The twelfth grade sells 13,483. How many tickets are left? 13. Manuel, a plumber, has several pieces of pipe on his truck. He has a 6-foot, 7-foot, 9foot, and 13-foot piece. If he uses 5 feet of pipe on a job, how many feet of pipe are left? 14. During inventory, the librarian finds that of the 2,482 books on the shelves, 482 are biographies, 726 are art books, and 534 are mysteries. The rest are fiction stories. How many books are fiction stories? 15. Twenty-five thousand, four hundred minus eleven thousand, three hundred seventy-eight.
SKILL #3: MULTIPLICATION 1. 222 x 22 2. 1,103 x 112 3. 2,963 x 6,291 4. 6,345 x 504 5. 10,782 x 409 6. Find the product of 803 and 4,034
7. 8. 9. 10. 11. 12. 13.
14. 15.
What is the result of 178 times 6,307? Find the product of 4,600 and 2,030 and round the answer to the nearest hundreds place. Triple 34,303 Double 150,000 James decides to save $15 a week. With 52 weeks in a year, how much will he have saved by the end of the year? The family’s new hybrid automobile is getting 45 miles on a gallon of gas. How many miles can be traveled on a total of 200 gallons? Noah is totaling the amount of money collected from ticket sales for the drama club’s play. They sold 506 tickets for $7 at the student price and 248 for $9 at the adult price. What is the total amount of money they collected? Each ream of printer paper contains 500 sheets. How many sheets of paper are contained in 19 reams of paper? Laura’s cat has 5 kittens. Each kitten eats 3 ounces of kitten food per day. How many ounces of food do the five kittens each in a 7-day period?
SKILL #4: DIVISION 1. 4,550 7 2.
2,760 23
3.
21,730 53
4.
28,080 72
5.
12,208 28
6. 7. 8. 9. 10. 11.
29,056 divided by 32 7,777 divided by 11 8,811 divided by 99 19 divided into 15,238 29 divided into 14,674 Nameesh has a job after school. He earned $868 over a 14-week period. What is Nameesh’s average weekly salary? Because of a huge thunderstorm causing flash flooding, Jake worked with his father filling 45-pound bags with sand to create a protective barrier around their business. If 5,580 pounds of sand were bagged, what was the total number of bags prepared? Adam’s car gets 23 miles on a gallon of gas. How many gallons will he use to take a 4,715-mile trip? The seventh graders took a field trip to a cotton farm in Greenwood, MS. If there were 245 students and chaperones travelling by buses with a 36-passenger capacity each, how many buses must be leased for the trip? The airplane leaves Burtonville at 2 p.m. and arrives at Meadowfield 1,095 miles away at 5 p.m. Find the average speed of the airplane in miles per hour.
12.
13. 14.
15.
Operations with Decimals SKILL #5: ADDITION 1. 78 + 0.045 2. 2.34 + 10 + 14.599 3. 7 + 0.346 + 12.8 + 4.036 4. 0.304 + 8.9 + 34.447 5. The sum of 42.06 + 6.7 + 17 + 0.009 6. The sum of 22 + 0.22 + 0.222 7. One rainy week, it rains 2.5 inches on Monday, 1.63 inches on Tuesday, and 3 inches on Wednesday. What is the total rainfall for these three days? 8. Terrell goes to the store and buys apples costing $2.95, a sports drink for $1.75, 2 energy bars for $3.53 together and all with tax included. How much did he spend at the store? If he paid with a $20 bill, how much money was left? 9. Juan delivers fliers announcing the upcoming community center carnival after school for three days. He walks 2.3 miles on Monday, 2.45 miles on Tuesday, and 5 miles on Wednesday. What is the total distance that Juan walks? 10. Corey’s dog Max, has three puppies. Their weights are 8.2 ounces, 5.12 ounces, and 6 ounces. What is their total weight? SKILL #6: SUBTRACTION 1. 12.5 – 4.2 2. 326 – 1.089 3. 144 – 78.24 4. 0.899 – 0.888 5. 5.6 – 0.6 6. From 235.01 subtract 0.999 7. From 3.83 subtract 0.83 8. Take away 2.3 from 8 9. Subtract 0.35 from 13.7 10. Take 0.99 from 8 11. Marco weighs 135 pounds before he goes on his sugar-free diet. He loses 5.6 pounds. How much does he weight after the diet? 12. Marshall purchases a pair of skates for $128.55 including tax. He gives the salesperson 5 $20s and 3 $10s. How much change does he receive? 13. To prepare for a party at the end of the school year, Soun Lee buys sodas for $5.98, chips for $10.35, dip for $4 and candy for $9.90. How much change does he receive from $35?
14.
15.
Michael earns $125 on Saturday for cutting 5 lawns. His expenses include $4.50 for gasoline and $20 for paying his younger brother to help, and setting aside $25 for his savings account. How much did he have left over? To play lacrosse, Chandler purchased the necessary equipment including $98 for the stick, $45.50 for the pads and another $105.30 for the helmet. How much was left out of $250 allotted by his parent for the entire purchase?
SKILL #7: MULTIPLICATION 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
77 x 0.11 24.2 x 944 0.12 x 1.1 2.73 x .069 5.6 x .98 0.0067 times 48.8 32 times 0.004 0.021 tripled The product of 1.035 and 0.25 To the nearest cent what is the cost of 1.6 pounds of grapes at $0.93 per pound? What is the total length of 65 pieces of ribbon each 0.2 m long? If the deli sells hummus at $5.30 per pound, find the cost of 3.5 pounds. What is the total cost of 128 metal washers selling for $0.07 each? What is the total length of 7 pieces of pipe each 0.04 foot long? What is the total distance traveled at 35 mph for 0.6 hour?
SKILL #8: DIVISION 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
1 5 17.6 0.32 2.7 9 0.235 0.005 0.00532 0.014 The quotient of 0.09 and 0.004 5 divided by 0.4 4.5 divided into 145.35 The quotient of 250 and 0.25 0.12 divided into 7.212 Divide the sum of 8.5 and 5.3 by 2 Divide the difference of 14.3 and 9.28 by 4 Divide the product of 0.21 and 2.5 by 3.5. Divide 76.02 by 3 and add 4.374 to the answer
15. 16. 17. 18. 19. 20.
Divide the sum of 8.4 and 7.47 by 2.3 Jeffrey buys some picture frame wire for $3.30. If the wire costs $.60 cents per foot, then how many feet of wire does he buy? Carl buys a 7.4-pound roast for $32.56. What is the cost of the roast per pound? A plane flies 1,305.9 miles in 3 hours. What is the plane’s average speed? A plane flies 858.2 miles in 2.8 hours. What is the plane’s average speed? If a cyclist travels 60.5 miles over a 5-hour period, what is his average speed per hour?
Operations with Fractions SKILL #9: CONVERT FROM IMPROPER FRACTION TO MIXED NUMBER IN SIMPLEST FORM 1.
22 16
2.
45 9
3.
66 13
4.
54 7
5.
121 55
6.
300 200
SKILL #10: CONVERT FROM MIXED NUMBER TO IMPROPER FRACTION 1.
3
1 2
2.
12
1 7
3.
15
2 5
4.
4
7 9
5.
16
3 4
6.
10
9 10
SKILL #11: ADDITION OF FRACTIONS WITH LIKE DENOMINATORS. Give answer in simplest form. 1.
3 7 12 12
2.
3 4 14 14
3.
1 5 6 6
4.
1 8 15 15
5.
11 7 24 24
6.
8 3 22 22
SKILL #12: ADDITION OF FRACTIONS WITH UNLIKE DENOMINATORS. Give answer in simplest form. 1.
3 1 8 2
2.
2 1 3 2
3.
2 4 3 5
4.
2 3 7 8
5.
3 1 5 6
6.
5 3 12 5
SKILL #13: ADDITION OF MIXED NUMBERS, WHOLE NUMBERS, AND FRACTIONS. Give answer in simplest form. 7 2 14 14
1.
9
4.
15 2
1 3
2.
1 2 2 2 9
3.
4
1 3 2 10 4
5.
1 2 7 3 5 7
6.
3 24 5 8
SKILL #14: SUBTRACTION OF FRACTIONS WITH LIKE AND UNLIKE DENOMINATORS with and without regrouping. Give answer in simplest form. 1.
5 5 3 8 8
4.
19 2
3 8
2.
18
7 4 15 15
3.
9
5.
4 2 15 13 9 9
6.
50
4 5
5 2 45 12 3
SKILL #15: MULTIPLICATION OF FRACTIONS. Simplify before you multiply where possible. Simplify all answers to lowest terms. 5 16
2.
1 10 2 17
3.
3 8 3 4 15
2 3
5.
4 1 3 2 5 2
6.
2 2 1 4 7 3
1.
8
4.
6 1
SKILL #16: DIVISION OF FRACTIONS. Remember to multiply by the reciprocal of the divisor. Express all answers in simplest form. 1.
8
4 5
2.
9 7 2 10
3.
3 5 3 4 8
4.
6
3 5
5.
4 38 3 5 25
6.
2
4 2 4 12 3
Rising 7th Grade Summer 2012 Mathematics Packet Welcome to 7th grade mathematics at Woodward Academy’s Middle School! The following packet comprises of several sections, each with a descriptive heading and performance objective. Mastery of all concepts is necessary for success in 7th grade math and completion of this packet is mandatory for all students. You should complete this packet without the use of a calculator and show all steps used to arrive at your final answer. During the first week of school, you will turn in your completed review packet and take a diagnostic test. Please keep in mind while you are working on this review packet that you will not be allowed to use a calculator during the assessment in August. We look forward to seeing you in August!
Skill #1: Decimals and Place Value Students will be able to determine place value of a given digit. Write the value of the underlined digit 1) 842,976 2) 761.0325
3) Write seven and ninety-six thousandths as a decimal.
4) Write 9.204 in words.
5) Write 0.0000073 in words.
Skill #2: Comparing and Ordering Decimals Students will be able to compare decimals and order decimals from least to greatest. Write the decimals in order from least to greatest. 6) 7.21 0.712 72.1 0.721
7) 0.01010
0.10101
0.01001
0.00101
Compare using >, Skill #3: Rounding 10) 15,763.75 11) 96.4 12) 120 13) 2,350,000 14) 287.2611 Skill #4: Adding & Subtracting Decimals 15) 30.96 16) 26.563 17) 1,432.242 18) 5.755 19) 64.792 20) 32.369 Skill #5: Multiplying Decimals 21) 0.000108 22) 84.24 23) 42.5154 24) 15.44 25) 2,396.1
1
Skill #6: Dividing Decimals by Whole Numbers 26) 4.2 27) 0.0027 28) 735,400 29) 11.8 Skill #7: Dividing Decimals by Decimals 30) 0.93 31) 0.0039 32) 7,900 33) 0.0021 34) 1,829,000 Skill #8: Multiplying & Dividing by Powers of Ten 35) 735,400 36) 0.06357 37) 56,970 38) 0.009645 39) 56 Skill #9: Mixed Numbers & Improper Fractions Converting Mixed Numbers to Improper Fractions 46 40) 7 79 41) 8 61 42) 5 38 43) 5 Converting Improper Fractions to Mixed Numbers 2 44) 3 3 4 45) 4 11 2 46) 2 3 1 47) 12 6 2 48) 2 7 2
Skill #10: Adding & Subtracting Fractions With Unlike Denominators 49) 50) 51) 52) 53)
1 8 46 63 1 2 5 11 6 16 1 46 8
1
Skill #11: Multiplying & Dividing Fractions 54) 55) 56) 57) 58) 59)
10 27 8 9 10 17 11 1 52 9 14 20 71 1 85
Skill #12: Drawing & Measuring Angles 60 – 61) Have a parent measure the angles you drew. 62) 1300 Skill #13: Comparing & Ordering Fractions 63) > 64) = 65) > 66) > 67)
1 1 2 9 , , , 4 2 3 12
3
Skill #14: Converting Between Fractions, Decimals & Percents 68) 0.35 69)
17 20
70) 71)
15.3% 0.8
72)
9 20
73)
60%
Skill #15: Comparing & Ordering Integers 74) -10 -8 -2 5 75) -101 -98 -15 0 98 135 Skill #16: Adding & Subtracting Integers 76) -7 77) -72 78) -63 79) -221 80) 116 81) -124
Skill #17: Perimeter & Area 82) P = 28 in A = 40 in 2 83) P = 36 cm A = 54 cm2 84) P = 60 mm A = 225 mm2 Skill #18: Unit Conversions 85) 36 ft 86) 12 qts 87) 3,000 meters 88) 12 hrs. 89) 200 cm 90) 5 yds.
4
Skill #19: Rates 91) 1 mile per minute 92) $2.15 93) 3. 3 feet per second 94) 83. 3 meters per minute Skill #20: Order of Operations 95) 5 96) 135 97) -11 98) -66 99) 3 100) 72
5
I.
ADDING MULTI-DIGIT NUMBERS AND DECIMALS 1) 827 + 2098
2) 32.45 + 606
3) 4165 + 24,149
4) 0.1414 + 77.275
5) 67.8903 + 2,395.789 + 23 + 4578
6) 89.79 + 1278 + 0.673 + 2309.3
II.
SUBTRACTING MULTI-DIGIT NUMBERS AND DECIMALS 1) 43,009 - 35,983
2) 2.098 - 1.34
3) 70,207.9 - 789.3
4) 3 - 0.089
III.
IV.
V.
VI.
MULTIPLICATION 1) 851 x 8
2) 828 x 35
3) 730 x 45
4) 282 x 787
MULTIPLYING DECIMALS 1) 9.2 x 0.74
2) 0.062 x 57
3) 3.6 x 0.0678
4) 12.34 x 1.048
DIVISION 1) 813 / 3
2) 924 / 77
3) 2,754 / 81
4) 24,620 / 240
DIVIDING DECIMALS. ROUND ANSWERS TO THE HUNDREDTHS PLACE. 1) 36.8 / 4
2) 4.28 / 70
3) 23.4 / 6.7
4) 34 / 8.9
VII.
ADDING FRACTIONS 1)
1 4 + = 6 6
2)
7 3 + = 8 8
3)
3 2 + = 10 5
4)
3 2 + = 4 3
VIII. SUBTRACT FRACTIONS
IX.
1)
7 3 − = 8 8
2)
9 3 − = 10 10
3)
3 1 − = 4 2
4)
7 3 − = 8 7
ADDING MIXED NUMBERS
1) 3
1 5 +2 = 12 12
2 4 3) 3 + 1 = 3 9
5 4 2) 2 + 1 = 6 6
1 1 4) 3 + 5 = 2 3
X.
SUBTRACTING MIXED NUMBERS
1 1) 8 − 6 = 5
2 2 3) 5 − 3 = 3 5
XI.
1 2 2) 5 − 3 = 5 5
1 4) 8 − 6 = 5
COMPARING AND ORDERING INTEGERS WRITE , OR = IN EACH BLANK.
1) -5 ___ 3
2) 25 ____ 2.5
3) -9 _____ -12
4) 133 ____ 13.3
5) -12 ____ -100
6) -77 _____ 77
PUT IN ORDER FROM LEAST TO GREATEST.
1) 35; -35; 3.5; 350
2) 23; 32; -23; 3.2
XII.
MEASURE AND CLASSIFY ANGLES. MEASURE EACH ANGLE, WRITE ITS MEASUREMENT, AND THEN CLASSIFY THE ANGLE AS RIGHT, ACUTE, OBTUSE, OR STRAIGHT.
1)
2)
3)
XIII. CONVERTING DECIMALS, FRACTIONS, AND PERCENTS DECIMAL
PERCENT
FRACTION
0.35 28% 0.04 1/2 8% 2 9/20
XIV. RATES
a. SUSIE WAS EXCITED SHE WAS GOING TO GET TO WORK AT HER FAVORITE ICE CREAM STORE OVER THE SUMMER. HER BOSS TOLD HER HE WOULD PAY HER $6.00 PER HOUR. USING THAT RATE OF PAY, COMPLETE THE TABLE BELOW. HOURLY PAY
HOURS WORKED
$6
1 2 4
$45
b. THE OLD TRUCK MR. JONES HAS GETS TERRIBLE GAS MILEAGE. BASED ON THE RATE GIVEN, FILL IN THE REST OF THE TABLE. MILES TRAVELED
GALLONS OF GAS USED 1 2
$60
5
$72 11
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Answers Page 1 1.
21.44
11. 0.1524
2.
4.32
3.
9.125
4.
11.52
12. 0.007632
13.
25.00368
7. 0.011
8. 0.201
3. 0.4
4. 2.25
14. 0.350056
5. 10.325 15 5.557463
Page 2 5.
6.123
6.
0.561
1.
$26.36
2. $4.85
Page 3 1. 8.75
2. 0.35
1. 8.02 hm per hour
2. 1.05 hours
Page 4
1. 5
7 10
10.
11
2.
1 18
5 12
3. 4
19 20
12. 3
17
11. 8
4.
5 16
11
1 4
1. 11 miles
9.
4
5 9
2. 10
1 hours 4
11. 5
1 3
Page 5 7. 48
12. 28
-
7 10
8. 4
1 2
9. 18
1. 4
7 gallons 9
2. 5
14 15
10. 20
20 21
5 hours 6
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Page 6
7. 1
3 5
8. 2
2 3
9.
8 9
1. 11 zippers
2. 20 jackets
1. x = 16
2. y = 9
3. m = 15
9. r = 3
1. a + 35 = 100 2. 4x = 100 a = 65 X = 25
12. 2
2 7
10.
9 32
11. 3
1 3
Page 7 7. b = 0.75
8. n = 120
4. AB, BC,
5. ∠AOB ,
CD, DE, EF
∠BOE , ∠EOF ,
Page 8 1. x = 4
2. y = 45
3. w = 5
Page 9 Answers can vary, suggestions listed 1. AO, BO,
2. AE, BF
3. AE, BF,
EO, FO
CD
∠FOA
6. ∠FOA and
7.
8.
∠BOE ; or
10 feet
6 inches
∠AOB and
7.2 meters
9 cm
∠EOF
54.5 miles
4.5 yards
Page 10 1. 188.4 cm
2. 21.98 cm
Page 11 1. 50.24 in2
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2. 1808.64 ft2
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Page 12 1. 2100 ft2
2. 120,000 yd2
3. 237.16 mi2
4. 1,620 in2
5. 3,360 in2
2. 48 cm2
4. 22.5 km2
5. 54 cm2
1. (3,4)
2. (5, -6)
3. (-6, -5)
4. (-3, 8)
5. (0,1)
1. C
2. L
3. K
4. H
5. A
1. B
2. H
3. A
4. G
5. A
6. H
7. C
8. J
1. C
2. F
3. C
4. J
5. A
6. J
7. D
8. J
1. A
2. H
3. D
4. G
5. C
6. H
7. C
6. 4.5 inches Page 13 1. 17.5 m2 Page 14
6. J Page 16
Page 18
Page 20
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Page 22 1. 6
2. 2
3. 8
4. 13
5. 50
6. 60
7. 90
8. 24
9. 21
10. 12
11. C
12. G
13. D
14. H
15. A
2. 21
3. 57.67
4. 24
5. 1.98
Page 23 1. 20.24 6. 46.55
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This is a 12-day review that will help you to remember some of the math concepts covered during the 6th grade year. It is to be completed over the summer and given to your 7th grade math teacher on the first day of school. Put this in a place that you will not lose it. Then, in August, spend a little time each day answering the questions. Everyone must complete the review, so do not throw it away and assume that you will not be responsible for it.
Helpful tips:
When adding or subtracting whole numbers or decimals, line up the place values.
When adding or subtracting fractions, get a common denominator.
When multiplying or dividing mixed numbers, put them into improper fractions first.
When dividing fractions, do not forget to change the sign to multiplication and make the second fraction its reciprocal.
Factors are numbers that can be evenly divided into a number…the factors of 6 are 1, 2, 3 and 6.
Multiples are the product of a number and any other number…some multiples of 5 are 0, 5, 10, etc.
To change a fraction into a decimal, divide the numerator by the denominator.
To change a decimal to a fraction, put the number over the place value of the last digit and reduce.
To change a fraction or decimal into a percent, multiply by 100.
To change a percent into a fraction or decimal, divide by 100.
NO CALCULATORS ARE TO BE USED!!!!!
Good luck and see you next year!
th
th
2010, 6 to 7 Grade Summer Review Packet
2
Day 1
1) Round 45.972 to the nearest tenth.
2) >, , , , , , , ,
SKILL #3: MULTIPLICATION 1. 222 x 22 2. 1,103 x 112 3. 2,963 x 6,291 4. 6,345 x 504 5. 10,782 x 409 6. Find the product of 803 and 4,034
7. 8. 9. 10. 11. 12. 13.
14. 15.
What is the result of 178 times 6,307? Find the product of 4,600 and 2,030 and round the answer to the nearest hundreds place. Triple 34,303 Double 150,000 James decides to save $15 a week. With 52 weeks in a year, how much will he have saved by the end of the year? The family’s new hybrid automobile is getting 45 miles on a gallon of gas. How many miles can be traveled on a total of 200 gallons? Noah is totaling the amount of money collected from ticket sales for the drama club’s play. They sold 506 tickets for $7 at the student price and 248 for $9 at the adult price. What is the total amount of money they collected? Each ream of printer paper contains 500 sheets. How many sheets of paper are contained in 19 reams of paper? Laura’s cat has 5 kittens. Each kitten eats 3 ounces of kitten food per day. How many ounces of food do the five kittens each in a 7-day period?
SKILL #4: DIVISION 1. 4,550 7 2.
2,760 23
3.
21,730 53
4.
28,080 72
5.
12,208 28
6. 7. 8. 9. 10. 11.
29,056 divided by 32 7,777 divided by 11 8,811 divided by 99 19 divided into 15,238 29 divided into 14,674 Nameesh has a job after school. He earned $868 over a 14-week period. What is Nameesh’s average weekly salary? Because of a huge thunderstorm causing flash flooding, Jake worked with his father filling 45-pound bags with sand to create a protective barrier around their business. If 5,580 pounds of sand were bagged, what was the total number of bags prepared? Adam’s car gets 23 miles on a gallon of gas. How many gallons will he use to take a 4,715-mile trip? The seventh graders took a field trip to a cotton farm in Greenwood, MS. If there were 245 students and chaperones travelling by buses with a 36-passenger capacity each, how many buses must be leased for the trip? The airplane leaves Burtonville at 2 p.m. and arrives at Meadowfield 1,095 miles away at 5 p.m. Find the average speed of the airplane in miles per hour.
12.
13. 14.
15.
Operations with Decimals SKILL #5: ADDITION 1. 78 + 0.045 2. 2.34 + 10 + 14.599 3. 7 + 0.346 + 12.8 + 4.036 4. 0.304 + 8.9 + 34.447 5. The sum of 42.06 + 6.7 + 17 + 0.009 6. The sum of 22 + 0.22 + 0.222 7. One rainy week, it rains 2.5 inches on Monday, 1.63 inches on Tuesday, and 3 inches on Wednesday. What is the total rainfall for these three days? 8. Terrell goes to the store and buys apples costing $2.95, a sports drink for $1.75, 2 energy bars for $3.53 together and all with tax included. How much did he spend at the store? If he paid with a $20 bill, how much money was left? 9. Juan delivers fliers announcing the upcoming community center carnival after school for three days. He walks 2.3 miles on Monday, 2.45 miles on Tuesday, and 5 miles on Wednesday. What is the total distance that Juan walks? 10. Corey’s dog Max, has three puppies. Their weights are 8.2 ounces, 5.12 ounces, and 6 ounces. What is their total weight? SKILL #6: SUBTRACTION 1. 12.5 – 4.2 2. 326 – 1.089 3. 144 – 78.24 4. 0.899 – 0.888 5. 5.6 – 0.6 6. From 235.01 subtract 0.999 7. From 3.83 subtract 0.83 8. Take away 2.3 from 8 9. Subtract 0.35 from 13.7 10. Take 0.99 from 8 11. Marco weighs 135 pounds before he goes on his sugar-free diet. He loses 5.6 pounds. How much does he weight after the diet? 12. Marshall purchases a pair of skates for $128.55 including tax. He gives the salesperson 5 $20s and 3 $10s. How much change does he receive? 13. To prepare for a party at the end of the school year, Soun Lee buys sodas for $5.98, chips for $10.35, dip for $4 and candy for $9.90. How much change does he receive from $35?
14.
15.
Michael earns $125 on Saturday for cutting 5 lawns. His expenses include $4.50 for gasoline and $20 for paying his younger brother to help, and setting aside $25 for his savings account. How much did he have left over? To play lacrosse, Chandler purchased the necessary equipment including $98 for the stick, $45.50 for the pads and another $105.30 for the helmet. How much was left out of $250 allotted by his parent for the entire purchase?
SKILL #7: MULTIPLICATION 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
77 x 0.11 24.2 x 944 0.12 x 1.1 2.73 x .069 5.6 x .98 0.0067 times 48.8 32 times 0.004 0.021 tripled The product of 1.035 and 0.25 To the nearest cent what is the cost of 1.6 pounds of grapes at $0.93 per pound? What is the total length of 65 pieces of ribbon each 0.2 m long? If the deli sells hummus at $5.30 per pound, find the cost of 3.5 pounds. What is the total cost of 128 metal washers selling for $0.07 each? What is the total length of 7 pieces of pipe each 0.04 foot long? What is the total distance traveled at 35 mph for 0.6 hour?
SKILL #8: DIVISION 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
1 5 17.6 0.32 2.7 9 0.235 0.005 0.00532 0.014 The quotient of 0.09 and 0.004 5 divided by 0.4 4.5 divided into 145.35 The quotient of 250 and 0.25 0.12 divided into 7.212 Divide the sum of 8.5 and 5.3 by 2 Divide the difference of 14.3 and 9.28 by 4 Divide the product of 0.21 and 2.5 by 3.5. Divide 76.02 by 3 and add 4.374 to the answer
15. 16. 17. 18. 19. 20.
Divide the sum of 8.4 and 7.47 by 2.3 Jeffrey buys some picture frame wire for $3.30. If the wire costs $.60 cents per foot, then how many feet of wire does he buy? Carl buys a 7.4-pound roast for $32.56. What is the cost of the roast per pound? A plane flies 1,305.9 miles in 3 hours. What is the plane’s average speed? A plane flies 858.2 miles in 2.8 hours. What is the plane’s average speed? If a cyclist travels 60.5 miles over a 5-hour period, what is his average speed per hour?
Operations with Fractions SKILL #9: CONVERT FROM IMPROPER FRACTION TO MIXED NUMBER IN SIMPLEST FORM 1.
22 16
2.
45 9
3.
66 13
4.
54 7
5.
121 55
6.
300 200
SKILL #10: CONVERT FROM MIXED NUMBER TO IMPROPER FRACTION 1.
3
1 2
2.
12
1 7
3.
15
2 5
4.
4
7 9
5.
16
3 4
6.
10
9 10
SKILL #11: ADDITION OF FRACTIONS WITH LIKE DENOMINATORS. Give answer in simplest form. 1.
3 7 12 12
2.
3 4 14 14
3.
1 5 6 6
4.
1 8 15 15
5.
11 7 24 24
6.
8 3 22 22
SKILL #12: ADDITION OF FRACTIONS WITH UNLIKE DENOMINATORS. Give answer in simplest form. 1.
3 1 8 2
2.
2 1 3 2
3.
2 4 3 5
4.
2 3 7 8
5.
3 1 5 6
6.
5 3 12 5
SKILL #13: ADDITION OF MIXED NUMBERS, WHOLE NUMBERS, AND FRACTIONS. Give answer in simplest form. 7 2 14 14
1.
9
4.
15 2
1 3
2.
1 2 2 2 9
3.
4
1 3 2 10 4
5.
1 2 7 3 5 7
6.
3 24 5 8
SKILL #14: SUBTRACTION OF FRACTIONS WITH LIKE AND UNLIKE DENOMINATORS with and without regrouping. Give answer in simplest form. 1.
5 5 3 8 8
4.
19 2
3 8
2.
18
7 4 15 15
3.
9
5.
4 2 15 13 9 9
6.
50
4 5
5 2 45 12 3
SKILL #15: MULTIPLICATION OF FRACTIONS. Simplify before you multiply where possible. Simplify all answers to lowest terms. 5 16
2.
1 10 2 17
3.
3 8 3 4 15
2 3
5.
4 1 3 2 5 2
6.
2 2 1 4 7 3
1.
8
4.
6 1
SKILL #16: DIVISION OF FRACTIONS. Remember to multiply by the reciprocal of the divisor. Express all answers in simplest form. 1.
8
4 5
2.
9 7 2 10
3.
3 5 3 4 8
4.
6
3 5
5.
4 38 3 5 25
6.
2
4 2 4 12 3
Rising 7th Grade Summer 2012 Mathematics Packet Welcome to 7th grade mathematics at Woodward Academy’s Middle School! The following packet comprises of several sections, each with a descriptive heading and performance objective. Mastery of all concepts is necessary for success in 7th grade math and completion of this packet is mandatory for all students. You should complete this packet without the use of a calculator and show all steps used to arrive at your final answer. During the first week of school, you will turn in your completed review packet and take a diagnostic test. Please keep in mind while you are working on this review packet that you will not be allowed to use a calculator during the assessment in August. We look forward to seeing you in August!
Skill #1: Decimals and Place Value Students will be able to determine place value of a given digit. Write the value of the underlined digit 1) 842,976 2) 761.0325
3) Write seven and ninety-six thousandths as a decimal.
4) Write 9.204 in words.
5) Write 0.0000073 in words.
Skill #2: Comparing and Ordering Decimals Students will be able to compare decimals and order decimals from least to greatest. Write the decimals in order from least to greatest. 6) 7.21 0.712 72.1 0.721
7) 0.01010
0.10101
0.01001
0.00101
Compare using >, Skill #3: Rounding 10) 15,763.75 11) 96.4 12) 120 13) 2,350,000 14) 287.2611 Skill #4: Adding & Subtracting Decimals 15) 30.96 16) 26.563 17) 1,432.242 18) 5.755 19) 64.792 20) 32.369 Skill #5: Multiplying Decimals 21) 0.000108 22) 84.24 23) 42.5154 24) 15.44 25) 2,396.1
1
Skill #6: Dividing Decimals by Whole Numbers 26) 4.2 27) 0.0027 28) 735,400 29) 11.8 Skill #7: Dividing Decimals by Decimals 30) 0.93 31) 0.0039 32) 7,900 33) 0.0021 34) 1,829,000 Skill #8: Multiplying & Dividing by Powers of Ten 35) 735,400 36) 0.06357 37) 56,970 38) 0.009645 39) 56 Skill #9: Mixed Numbers & Improper Fractions Converting Mixed Numbers to Improper Fractions 46 40) 7 79 41) 8 61 42) 5 38 43) 5 Converting Improper Fractions to Mixed Numbers 2 44) 3 3 4 45) 4 11 2 46) 2 3 1 47) 12 6 2 48) 2 7 2
Skill #10: Adding & Subtracting Fractions With Unlike Denominators 49) 50) 51) 52) 53)
1 8 46 63 1 2 5 11 6 16 1 46 8
1
Skill #11: Multiplying & Dividing Fractions 54) 55) 56) 57) 58) 59)
10 27 8 9 10 17 11 1 52 9 14 20 71 1 85
Skill #12: Drawing & Measuring Angles 60 – 61) Have a parent measure the angles you drew. 62) 1300 Skill #13: Comparing & Ordering Fractions 63) > 64) = 65) > 66) > 67)
1 1 2 9 , , , 4 2 3 12
3
Skill #14: Converting Between Fractions, Decimals & Percents 68) 0.35 69)
17 20
70) 71)
15.3% 0.8
72)
9 20
73)
60%
Skill #15: Comparing & Ordering Integers 74) -10 -8 -2 5 75) -101 -98 -15 0 98 135 Skill #16: Adding & Subtracting Integers 76) -7 77) -72 78) -63 79) -221 80) 116 81) -124
Skill #17: Perimeter & Area 82) P = 28 in A = 40 in 2 83) P = 36 cm A = 54 cm2 84) P = 60 mm A = 225 mm2 Skill #18: Unit Conversions 85) 36 ft 86) 12 qts 87) 3,000 meters 88) 12 hrs. 89) 200 cm 90) 5 yds.
4
Skill #19: Rates 91) 1 mile per minute 92) $2.15 93) 3. 3 feet per second 94) 83. 3 meters per minute Skill #20: Order of Operations 95) 5 96) 135 97) -11 98) -66 99) 3 100) 72
5
I.
ADDING MULTI-DIGIT NUMBERS AND DECIMALS 1) 827 + 2098
2) 32.45 + 606
3) 4165 + 24,149
4) 0.1414 + 77.275
5) 67.8903 + 2,395.789 + 23 + 4578
6) 89.79 + 1278 + 0.673 + 2309.3
II.
SUBTRACTING MULTI-DIGIT NUMBERS AND DECIMALS 1) 43,009 - 35,983
2) 2.098 - 1.34
3) 70,207.9 - 789.3
4) 3 - 0.089
III.
IV.
V.
VI.
MULTIPLICATION 1) 851 x 8
2) 828 x 35
3) 730 x 45
4) 282 x 787
MULTIPLYING DECIMALS 1) 9.2 x 0.74
2) 0.062 x 57
3) 3.6 x 0.0678
4) 12.34 x 1.048
DIVISION 1) 813 / 3
2) 924 / 77
3) 2,754 / 81
4) 24,620 / 240
DIVIDING DECIMALS. ROUND ANSWERS TO THE HUNDREDTHS PLACE. 1) 36.8 / 4
2) 4.28 / 70
3) 23.4 / 6.7
4) 34 / 8.9
VII.
ADDING FRACTIONS 1)
1 4 + = 6 6
2)
7 3 + = 8 8
3)
3 2 + = 10 5
4)
3 2 + = 4 3
VIII. SUBTRACT FRACTIONS
IX.
1)
7 3 − = 8 8
2)
9 3 − = 10 10
3)
3 1 − = 4 2
4)
7 3 − = 8 7
ADDING MIXED NUMBERS
1) 3
1 5 +2 = 12 12
2 4 3) 3 + 1 = 3 9
5 4 2) 2 + 1 = 6 6
1 1 4) 3 + 5 = 2 3
X.
SUBTRACTING MIXED NUMBERS
1 1) 8 − 6 = 5
2 2 3) 5 − 3 = 3 5
XI.
1 2 2) 5 − 3 = 5 5
1 4) 8 − 6 = 5
COMPARING AND ORDERING INTEGERS WRITE , OR = IN EACH BLANK.
1) -5 ___ 3
2) 25 ____ 2.5
3) -9 _____ -12
4) 133 ____ 13.3
5) -12 ____ -100
6) -77 _____ 77
PUT IN ORDER FROM LEAST TO GREATEST.
1) 35; -35; 3.5; 350
2) 23; 32; -23; 3.2
XII.
MEASURE AND CLASSIFY ANGLES. MEASURE EACH ANGLE, WRITE ITS MEASUREMENT, AND THEN CLASSIFY THE ANGLE AS RIGHT, ACUTE, OBTUSE, OR STRAIGHT.
1)
2)
3)
XIII. CONVERTING DECIMALS, FRACTIONS, AND PERCENTS DECIMAL
PERCENT
FRACTION
0.35 28% 0.04 1/2 8% 2 9/20
XIV. RATES
a. SUSIE WAS EXCITED SHE WAS GOING TO GET TO WORK AT HER FAVORITE ICE CREAM STORE OVER THE SUMMER. HER BOSS TOLD HER HE WOULD PAY HER $6.00 PER HOUR. USING THAT RATE OF PAY, COMPLETE THE TABLE BELOW. HOURLY PAY
HOURS WORKED
$6
1 2 4
$45
b. THE OLD TRUCK MR. JONES HAS GETS TERRIBLE GAS MILEAGE. BASED ON THE RATE GIVEN, FILL IN THE REST OF THE TABLE. MILES TRAVELED
GALLONS OF GAS USED 1 2
$60
5
$72 11
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Answers Page 1 1.
21.44
11. 0.1524
2.
4.32
3.
9.125
4.
11.52
12. 0.007632
13.
25.00368
7. 0.011
8. 0.201
3. 0.4
4. 2.25
14. 0.350056
5. 10.325 15 5.557463
Page 2 5.
6.123
6.
0.561
1.
$26.36
2. $4.85
Page 3 1. 8.75
2. 0.35
1. 8.02 hm per hour
2. 1.05 hours
Page 4
1. 5
7 10
10.
11
2.
1 18
5 12
3. 4
19 20
12. 3
17
11. 8
4.
5 16
11
1 4
1. 11 miles
9.
4
5 9
2. 10
1 hours 4
11. 5
1 3
Page 5 7. 48
12. 28
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7 10
8. 4
1 2
9. 18
1. 4
7 gallons 9
2. 5
14 15
10. 20
20 21
5 hours 6
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Page 6
7. 1
3 5
8. 2
2 3
9.
8 9
1. 11 zippers
2. 20 jackets
1. x = 16
2. y = 9
3. m = 15
9. r = 3
1. a + 35 = 100 2. 4x = 100 a = 65 X = 25
12. 2
2 7
10.
9 32
11. 3
1 3
Page 7 7. b = 0.75
8. n = 120
4. AB, BC,
5. ∠AOB ,
CD, DE, EF
∠BOE , ∠EOF ,
Page 8 1. x = 4
2. y = 45
3. w = 5
Page 9 Answers can vary, suggestions listed 1. AO, BO,
2. AE, BF
3. AE, BF,
EO, FO
CD
∠FOA
6. ∠FOA and
7.
8.
∠BOE ; or
10 feet
6 inches
∠AOB and
7.2 meters
9 cm
∠EOF
54.5 miles
4.5 yards
Page 10 1. 188.4 cm
2. 21.98 cm
Page 11 1. 50.24 in2
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2. 1808.64 ft2
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Page 12 1. 2100 ft2
2. 120,000 yd2
3. 237.16 mi2
4. 1,620 in2
5. 3,360 in2
2. 48 cm2
4. 22.5 km2
5. 54 cm2
1. (3,4)
2. (5, -6)
3. (-6, -5)
4. (-3, 8)
5. (0,1)
1. C
2. L
3. K
4. H
5. A
1. B
2. H
3. A
4. G
5. A
6. H
7. C
8. J
1. C
2. F
3. C
4. J
5. A
6. J
7. D
8. J
1. A
2. H
3. D
4. G
5. C
6. H
7. C
6. 4.5 inches Page 13 1. 17.5 m2 Page 14
6. J Page 16
Page 18
Page 20
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Page 22 1. 6
2. 2
3. 8
4. 13
5. 50
6. 60
7. 90
8. 24
9. 21
10. 12
11. C
12. G
13. D
14. H
15. A
2. 21
3. 57.67
4. 24
5. 1.98
Page 23 1. 20.24 6. 46.55
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This is a 12-day review that will help you to remember some of the math concepts covered during the 6th grade year. It is to be completed over the summer and given to your 7th grade math teacher on the first day of school. Put this in a place that you will not lose it. Then, in August, spend a little time each day answering the questions. Everyone must complete the review, so do not throw it away and assume that you will not be responsible for it.
Helpful tips:
When adding or subtracting whole numbers or decimals, line up the place values.
When adding or subtracting fractions, get a common denominator.
When multiplying or dividing mixed numbers, put them into improper fractions first.
When dividing fractions, do not forget to change the sign to multiplication and make the second fraction its reciprocal.
Factors are numbers that can be evenly divided into a number…the factors of 6 are 1, 2, 3 and 6.
Multiples are the product of a number and any other number…some multiples of 5 are 0, 5, 10, etc.
To change a fraction into a decimal, divide the numerator by the denominator.
To change a decimal to a fraction, put the number over the place value of the last digit and reduce.
To change a fraction or decimal into a percent, multiply by 100.
To change a percent into a fraction or decimal, divide by 100.
NO CALCULATORS ARE TO BE USED!!!!!
Good luck and see you next year!
th
th
2010, 6 to 7 Grade Summer Review Packet
2
Day 1
1) Round 45.972 to the nearest tenth.
2) >, , , , , , , ,
