SOUTH MIDDLE SCHOOL SUMMER MATH PACKET 2014

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

periodically over the summer. Mrs. Freeman: rfreeman@braintreema.gov Mrs. Norton: knorton@braintreema.gov Mr. Boynton: eboynton@braintreema.gov

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.

What are the place values?

10,000’s Thousands Hundreds Tens Ones . Tenths Hundredths Thousandths 10,000ths

Examples:

1. 7.9+10.12

Line up the decimals.

7.9+10.12

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,

24 Greatest Common Factor: 8 16÷8=2 24÷8=3

Answer: 23

2.4860

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Greatest Common Factor: 12 48÷12=4 60÷12=5

Answer: 45

Improper Fractions and Mixed Numbers

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. 527

7×5=35 35+2=37 The numerator is 37. The denominator is still 7.

Answer: 377

2. 10111

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: 12510

=12 12

Fraction Exercises: Part 1 – Must Show Work for Full Credit

Simplify the following fractions or mixed numbers.

51.912

52.315

53.1020

54.8498

55. 815105

56. 9250375

Change each mixed number into an improper fraction.

57. 215

58. 635

59. 915

60. 15 78

Change each improper fraction into a mixed number.

61.547

62.325

63. 275

64.739

65. 1574

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+ 25

45+ 25=4+25

=65=1 15

Answer: 115

2. 214−34

Since 3 is greater than 1, borrow a whole from 2 → 214=1 5

4

1 54−34=1 5−3

4=1 24=1 12

Or, change 214 into an improper fraction → 2

14=94

94−34=9−3

4=64=1 2

4=1 12

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:

1.45−27

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=4×75×7

=2835

27=2×57×5

=1035

Solve.

2835

+ 1035

=28+1035

=3835

=1 335

Answer: 1335

2. 116+2 38

Find the least common multiple:

6 → 6, 12, 18, 24, 30… 8 → 8, 16, 24, 32…

LCM: 24

Rewrite the fractions:

1 16=1 1×46×4

=1 424

2 38=2 3×38×3

=2 924

Solve.

1 424

+2 924

=3 4+924

=3 1324

Answer: 31324

Multiplying and Dividing Fractions

Multiplying:o It does not matter whether the fractions have the same denominator o Change all mixed numbers to improper fractions o Multiply the numerators o Multiply the denominatorso If possible: simplify and/or change improper fractions into mixed numberso Integer rules apply

Examples:

1.45∙ 38

Multiply the numerators, then the denominators.

4 ∙35 ∙8

=1240

Simplify if possible

1240÷ 44= 310

Answer: 310

2. 125∙2 12

Change improper fractions to mixed numbers.75∙ 52

Then multiply as you did in example 1

7 ∙55 ∙2

=3510

Simplify

3510÷ 55=72

Change all improper fractions back to mixed numbers

72=3 12 Answer: 3

12

Dividing:o It does not matter whether the fractions have the same denominator o Change all mixed numbers to improper fractions o Multiply by the reciprocal

Hint: Keep, Change, Flipo If possible: simplify and/or change improper fractions into mixed numberso Integer rules apply

Examples:

1.27÷ 45

Keep the first fraction, flip the second fraction, and change division to multiplication.

27∙ 54

Follow multiplication rules.

2 ∙57 ∙4

=1028

Simplify if possible.1028÷ 22= 514

Answer: 514

2. 323÷1 15

Change all mixed numbers to improper fractions:

113÷ 65

Keep the first fraction, flip the second fraction, and change division to multiplication.

113∙ 56

Follow multiplication rules.

11 ∙53 ∙6

=5518

Simplify if possible, and change improper fractions back to mixed numbers.5518

=3 118

Answer: 3118

Fraction Exercises: Part 2 – Must Show Work for Full Credit

66.47+ 27

67. 59+ 49

68. 1112

+ 512

69. 910

− 310

70.34+ 78

71. 614+8 23

72. 12110

+7 56

73. 1878+15 5

8

74. 1437−10 1

2

75. 525−3 12+2 27

76.12∙ 34

77.13∙ 58

78.67∙ 23

79. 313∙1 34

80. 114∙2 25

81.920÷ 310

82.49÷ 35

83.916÷ 38

84. 512÷1 18

85. 723÷ 56

86. John walked 12 of a mile yesterday and

34 of a mile today. How many miles has John

walked?

87. 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?

88. A recipe requires 12 teaspoon cayenne pepper,

34 teaspoon black pepper, and

14 teaspoon

red pepper. How much pepper does this recipe need?

89. 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?

90. 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?

91. 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?

92. A recipe needs 34 teaspoon black pepper and

14 red pepper. How much more black pepper

does the recipe need?

93. 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?

94. 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?

95. 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?

96. One of the cats in the neighborhood had six kittens all about the same size. If each of the

new kittens weighed about 512 ounces, how much would all of the new kittens weigh?

97. A bunch of neighborhood kids went on a hike through the nature center. The total mileage

they walked was 1623 miles. If each kid contributed 4

16miles to the hike, how many kids

went on the hike?

98. Lynn has 15 different color markers in her new case. The total weight of all the markers in

the case is 3712ounces. If each marker is the same, how much does each of Lynn’s markers

weigh?

99. During the rainstorm last week Jackson and his sister wanted to see how much water they could collect from the rain. In order to do this they put out 12 three-and-a-half liter containers to catch the water in. If all the containers got filled four times, how many liters of water did they collect in all?

100. Jason was in the process of writing a story for a school contest. So far he has completed

10 12 pages of this story. On the average each page taken him 1

23hours to write. How much

time has Jason already put into writing his story?