SOUTH MIDDLE SCHOOL SUMMER MATH PACKET 2011 6 th to 7 th Grade To be completed by all students entering the 7 th grade at South Middle School. This is due the first day of school and will be graded. In order to receive full credit you must show ALL work. No work = No credit This packet is intended to review key concepts you learned in 6 th grade that are important for you to know in 7 th grade. The packet is broken into 3 sections: Decimal Operations Integer Operations Fractions Each section has notes and examples to help you if you get stuck. Still stuck? Try emailing us. We might not respond immediately , but we will check our email periodically over the summer. Mrs. Freeman: [email protected]Mrs. Norton: [email protected]Mr. Boynton: [email protected]Have a great summer and keep those math facts fresh! ~Mrs. Freeman, Mrs. Norton and Mr. Boynton Your future 7 th Grade Math Teachers
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SOUTH MIDDLE SCHOOL SUMMER MATH PACKET 2011
6th to 7th GradeTo be completed by all students entering the 7th grade at South Middle School.
This is due the first day of school and will be graded. In order to receive full credit you must show ALL work.
No work = No credit This packet is intended to review key concepts you learned in 6th grade that are important
for you to know in 7th grade. The packet is broken into 3 sections:
Decimal Operations Integer Operations Fractions
Each section has notes and examples to help you if you get stuck. Still stuck? Try emailing us. We might not respond immediately, but we will check our email
Have a great summer and keep those math facts fresh!
~Mrs. Freeman, Mrs. Norton and Mr. Boynton Your future 7th Grade Math Teachers
Lost your packet?If you lose your packet, the Thayer Public Library has a copy. Copies can also be downloaded online through the South Middle School website (under Mrs. Norton) or Mrs.
Freeman’s class website at https://sites.google.com/site/mrsfreemansclasswebsite/ under Forms and Docs.
Getting tutored this summer?If you are planning on getting tutored this summer, additional problems are available online. Visit the South Middle School website (under Mrs. Norton) or
Mrs. Freeman’s class website at https://sites.google.com/site/mrsfreemanclasswebsite/ under Forms and Docs.
Name _____________________________________________________ Due: First Day of School
South Middle School Math Summer Packet 6th to 7th Grade
Decimal Operations
Adding and Subtracting Decimals
Adding and subtracting decimals is like adding and subtracting whole numbers. BUT you must line up the decimal points and bring the decimal point down into the answer. Use zeros to hold place values if necessary.
Use a zero in the hundredths column to hold the place value.
7.90+10.12
Bring the decimal down and solve.
7.90+10.12 18 .02
Answer: 18.02
2. 428.31−37.4
Line up the decimals.
428.31- 37.4
Use a zero to hold the place value.
428.31- 37.40
Bring down the decimal and solve.
428.31- 37.40 390.91
Answer: 390.91
3. 101.101+989.8
Line up the decimals.
101.101+989.8
Use zeros to hold place values.
101.101+989.800
Bring the decimal down and solve.
101.101+989.8001090.901
Answer: 1,090.901
4. 1,234.5−6.789
Line up the decimals.
1,234.5 - 6.789
Use zeros to hold place values.
1,234.500- 6.789
Bring the decimal down and solve. 1,234.500- 6.7891,227.711
Answer: 1,227.711
Multiplying Decimals
Multiplying decimals is like multiplying whole numbers – it is not necessary to line up the decimals.
BUT don’t forget to put the decimal in the product – Count the number of decimal places in the original factors and move that many places from the right in the product.
Examples:
1. 6.7×12.3
Set up the problem and solve.
12.3 × 6.7
861 +7380
8241
Move decimal back in.
12.31 place × 6.71 place
861 +7380
82.412 places
Answer: 82.41
2. 4.201×9.3
Setup the problem and solve.
4.201 × 9.3 12603+ 378090 390693
Move decimal back in.
4.2013 places × 9.31 place 12603+ 378090 39.06934 places
Answer: 39.0693
Dividing Decimals
Change the divisor into a whole number by moving the decimal to the right of its last digit. Move the decimal to the right the same number of spaces in the dividend – use zeros as
place holders if necessary. Carry out the division. The decimal in the quotient (above the division bar) will be directly
above the decimal in the dividend (below the division bar).
Examples:
1. 151.56÷1.2
Setup the problem. 1.2)151.56
Move the decimal out of the divisor and move the decimal the same number of spaces in the in the dividend.
12)1515.6 moved 1 space
Please note it is okay to move the decimal above the quotient line at this time.
. moves straight up12)1515.6
Divide.
1263 12)1515.6 -12
31 -24 75 -72 36 -36 0
Make sure the decimal is put into the quotient.
126.312)1515.6
Answer: 126.3
2. 58÷0.725
Setup the problem.
0.725)58
Move the decimal out of the divisor and move the decimal the same number of spaces in the in the dividend.
725)58000. moved 3 spaces
Please note it is okay to move the decimal above the quotient line at this time.
. moves straight up725)58000.
Divide. 80 725)58000. -5800
00 - 0 0
Make sure the decimal is put into the quotient.
80.725)58000.
Answer: 80
Decimal Operations Exercises – Must Show Work for Full Credit
1. 1.387+2.3444
2. 0.7+87.8+8.174
3. 56.13−17.59
4. 826.7−24.6444
5. 4.63+7.71
6. 12.4−10.66
7. 19.055−4.41
8. 9.655×8.33
9. 12.75×91.3
10. 3.76×0.61
11. 0.24×0.3
12. 211.68÷9.8
13. 42.363÷8.1
14. 444.36÷ 4.8315. 0.7042÷0.07
16. The moon orbits the Earth in 27.3 days. How many orbits does the moon make in 365.25 days? Round to the nearest hundredth.
17. During summer vacation, the temperature reached a high of 95.3°F and a low of 62.8°F. What was the difference in temperature?
18. The school store has t-shirts on sale 4 for $12.32. If Sarah wants to buy 10 t-shirts, how much will it cost?
19. Apollo 11 astronauts Scott and Irwin drove the lunar rover about 26.4 km on the moon. Their average speed was 3.3 km/hr. How long did they drive the lunar rover?
20. Julia cut a string 8.46 meters long into 6 equal pieces. How long was each piece of string?
21. Marcus bought 8.6 kg of sugar. He poured the sugar equally into 5 bottles. There was 0.35 kg of sugar left over. How much sugar is in 1 bottle?
22. Peter bought a watermelon that was 2.3 lbs. Paul bought a watermelon that weighs 2.22 lbs. How much watermelon do they have in total?
23. Suzie has $20 to spend at the toy store and candy store. At the toy store she sees a doll for $9.67 and a board game for $5.15. How much money does she have left to spend at the candy store?
24. During Penny Wars, homeroom 213 had $123.25 in their bucket. Homeroom 206 had $132.09 in their bucket. How much money did they have altogether?
25. On a road trip, the Fribble family drove 345.34 miles in 5.2 hours. What was their average rate (miles per hour)?
Integer Operations
Adding Integers
If the signs are the same: Add the absolute values and keep the sign.
If the signs are different: Subtract the absolute values and take the sign of the greater absolute value.
Absolute value – the distance a number is from zero
Examples:
1. −9+ (−4 )
|−9|=9 |−4|=4 Signs are the same so, 9+4=13 Signs are the same (both
negative), so keep the sign negative.
Answer: −13
2. −25+13
|−25|=25 |13|=13 Signs are different so,
25−13=12 |−25|>|13| so the answer will be
negative
Answer: −12
Subtracting Integers
Change subtraction to addition and change the sign of the second number. Follow rules for addition. Slash and Dash or Slash-Slash
Examples:
1. 78−120
78+(−120 ) Signs are different, so:
|−120|−|78|=¿120−78=¿
42 |−120|>|78|, so answer is
negative
Answer: −42
2. 156−(−84)
156+(+84 ) Signs are the same, so:
|156|+|84|=¿156+84=¿
240 Both positive, so keep positive.
Answer: 240
Integer Operation Exercises – Must Show Work for Full Credit
26. 5−7
27. −9−(−4 )
28. 4+(−4 )
29. 0+ (−3 )
30. −20−32
31. −72+(−312 )
32. 100−101
33. −5−(−5 )
34. −2−8
35. 35+(−95 )
36. 89+129
37. −746+ (−9,200 )
38. 56−62
39. 123+(−456 )
40. 58−(−12 )
41. Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?
42. In Buffalo, New York the temperature was -14°F. If the temperature dropped 7°F, then what is the temperature now?
43. A submarine was 800 feet below sea level. If it rises 250 feet, what is the submarine’s new position?
44. Roman Civilization began in 509 B.C. and ended in 476 A.D. How long did Roman Civilization last?
45. One day in the Sahara Desert it was 136°F. That same day in the Gobi Desert it was -50°F. What is the difference between the two temperatures?
46. Anna’s bank account has $26. She wants to buy a shirt for $30. What would her bank account balance be if she buys the shirt?
47. The temperature at midnight was 2°F. At sunrise, the temperature was 5 degrees lower. What is the temperature?
48. The lowest recorded temperature in Puerto Rico was 60°F. The lowest recorded temperature in Fairbanks, Alaska was -62°F. What is the difference between these two temperatures?
49. David and Lisa played a game. David scored -150 points and Lisa scored -450 points. How many points did they score all together?
50. Use #49. Maya also played the game. She scored 350 points. What is the combined score for all three people?
Fractions
Simplifying Fractions
Simplifying fractions means to divide the numerator and denominator by the same number so that the numerator and denominator are as small or as simple as possible.
To simplify, find the greatest common factor (GCF). GCF – the greatest factor that both numbers have in common.
List out the factors of the numerator
List out the factors of the denominator The greatest factor that they have in common is the GCF.
Divide the numerator and denominator by the GCF.
Examples:
1.1624
Factors of 16: 1, 2, 4, 8, 16 Factors of 24: 1, 2, 3, 4, 6, 8, 12,
To change a mixed number into an improper fraction complete the following steps:
Multiply the whole number by the denominator. Add the product to the numerator. Write the sum as your new numerator. Keep the same denominator as the original fraction.
Examples:
1. 5 27
7×5=35 35+2=37 The numerator is 37. The denominator is still 7.
Answer: 377
2. 10 111
11×10=110 110+1=111 The numerator is 111.
The denominator is still 11.
Answer: 11111
To change an improper fraction into a mixed number complete the following steps:
1. Divide the numerator by the denominator.2. The number of times the denominator “goes into” the numerator is the whole number.3. The remainder is the new numerator.4. Keep the denominator the same and simplify if necessary.
Examples:
1.587
58÷7 7 “goes into” 58, 8 times, so 8 is
the whole number. There are 2 leftover, so 2 is the
numerator The denominator is still 7.
Answer: 827
2.12510
125÷10 10 “goes into” 125, 12 times, so
12 is the whole number There are 5 leftover, so 5 is the
numerator. The denominator is still 10.
Answer: 12 510
=12 12
Fraction Exercises: Part 1 – Must Show Work for Full Credit
Simplify the following fractions or mixed numbers.
51.416
52.912
53.3
15
54.1020
55.1218
56.2763
57.8498
58. 6 2440
59. 8 15105
60. 9 250375
61.2799
62.228981
63.552882
64.3751
65.19152
Change each mixed number into an improper fraction.
66. 2 15
67. 6 35
68. 7 12
69. 9 15
70. 15 78
Change each improper fraction into a mixed number.
71.547
72.325
73. 275
74.739
75. 157
4
Add and Subtracting Fractions
Adding and Subtracting Like Fractions
Like Fractions are fractions with the same denominator. Add or subtract the numerators and keep the same denominator.
If the sum or difference is an improper fraction make sure to rewrite the answer as a mixed number.
Don’t forget: It is possible to borrow a whole from the whole number if the first numerator is smaller than the second numerator when subtracting.
To avoid confusion, change all mixed numbers into improper fractions and deal only with the numerators.
Examples:
1.45+ 2
5
45+ 2
5=4+2
5=6
5=1 1
5
Answer: 115
2. 2 14−3
4
Since 3 is greater than 1, borrow a whole from 2 → 214=1 5
4
1 54−3
4=1 5−3
4=1 2
4=1 1
2
Or, change 214 into an improper fraction → 2
14=9
4
94−3
4=9−3
4=6
4=1 2
4=1 1
2
Answer: 112
Adding and Subtracting Unlike Fractions
Unlike Fractions are fractions with different denominators. First find equivalent fractions with the same denominator.
To do this, find the least common multiple (LCM). Rewrite the fractions with the LCM as the denominator.
Don’t forget to rewrite the numerators. Now that the fractions are written as like fractions, follow rules for like fractions.
Examples:
1.45−2
7
Find the least common multiple:
5 → 5, 10, 15, 20, 25, 30, 35, 40, 45…
7 → 7, 14, 28, 35, 42…
LCM: 35
Rewrite the fractions:
45=4×7
5×7=28
35
27=2×5
7×5=10
35
Solve.
2835
+ 1035
=28+1035
=3835
=1 335
Answer: 1335
2. 1 16+2 3
8
Find the least common multiple:
6 → 6, 12, 18, 24, 30… 8 → 8, 16, 24, 32…
LCM: 24
Rewrite the fractions:
1 16=1 1×4
6×4=1 4
24
2 38=2 3×3
8×3=2 9
24
Solve.
1 424
+2 924
=3 4+924
=3 1324
Answer: 31324
Fraction Exercises: Part 2 – Must Show Work for Full Credit
76.47+ 2
7
77. 59+ 4
9
78. 1112
+ 512
79. 9
10− 3
10
80. 9
16− 3
16
81.34+ 7
8
82. 614+8 2
3
83. 1112
+ 49
84. 12 110
+7 56
85. 18 78+15 5
8
86. 1423−12
87. 14 37−10 1
2
88. 16 38−2 5
6
89. 47+ 2
3−4
5
90. 525−3 1
2+2 2
7
91. John walked 12 of a mile yesterday and
34 of a mile today. How many miles has John
walked?
92. Mary is preparing a final exam. She study 32 hours on Friday,
64 hours on Saturday, and
23
hour on Sunday. How many hours did she study over the weekend?
93. A recipe requires 12 teaspoon cayenne pepper,
34 teaspoon black pepper, and
14 teaspoon
red pepper. How much pepper does this recipe need?
94. A football player advances 23 of a yard. A second player in the same team advances 5
14
yards. How many more yards did the second player advance?
95. John lives 38 mile from the Museum of Science. Sylvia lives
14 mile from the Museum of
Science. How much closer is Sylvia from the museum?
96. Ted used the amounts of spices listed below to make a pie.
2 teaspoons of cinnamon
34
teaspoon of nutmeg
12
teaspoon of cloves
What is the total number of teaspoons of spices that Ted used?
97. A recipe needs 34 teaspoon black pepper and
14 red pepper. How much more black pepper
does the recipe need?
98. Amy used 212 cans of chicken broth to make soup. Each can contained 7
12 ounces of broth.
What was the total number of ounces of chicken broth that Amy used?
99. A carpenter cuts a board that is 412 feet long. After the cut, 1
38 feet remain. How long was
the piece that was cut?
100. Bill and Andy were racing to see who could run the farthest in 5 minutes. Bill ran 58 of a
mile, and Andy ran 34 of a mile. How much farther did Andy run than Bill?