To Be Completed by All Students Entering the 7Th Grade at South Middle School

SOUTH MIDDLE SCHOOL

SUMMER MATH PACKET 2011

6th to 7th Grade

To 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 conceptsyou 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:
Mrs. Norton:

Have a great summer and keep those math facts fresh!

Mrs. Freeman and Mrs. Norton

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 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 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:

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

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

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

+989.800

1090.901

Answer: 1,090.901

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

- 6.789

1,227.711

Answer: 1,227.711

Multiplying Decimals

Multiplying decimals is like multiplying whole numbers – it is not necessary to line up the decimals.
BUTdon’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:

Set up the problem and solve.

12.3

× 6.7

861

+7380

8241

Move decimal back in.

12.31 place

× 6.71 place

861

+7380

82.412 places

Answer: 82.41

Setup the problem and solve.

4.201

× 9.3

12603

+ 378090

390693

Move decimal back in.

4.2013 places

× 9.31 place

12603

+ 378090

39.06934 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:

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 up

12)1515.6

Divide.

1263

12)1515.6

-12

-24

-72

-36

Make sure the decimal is put into the quotient.

126.3

12)1515.6

Answer: 126.3

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 up

725)58000.

Divide.

725)58000.

-5800

- 0

Make sure the decimal is put into the quotient.

80.

725)58000.

Answer: 80

Decimal Operations Exercises – Must Show Work for Full Credit

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.

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?

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?

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?

Julia cut a string 8.46 meters long into 6 equal pieces. How long was each piece of string?

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?

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?

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?

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?

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:

Signs are the same so,
Signs are the same (both negative), so keep the sign negative.

Answer:

Signs are different so,
so the answer will be negative

Answer:

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:

Signs are different, so:

, so answer is negative

Answer:

Signs are the same, so:

Both positive, so keep positive.

Answer:

Integer Operation Exercises – Must Show Work for Full Credit

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?

In Buffalo, New York the temperature was -14°F. If the temperature dropped 7°F, then what is the temperature now?

A submarine was 800 feet below sea level. If it rises 250 feet, what is the submarine’s new position?

Roman Civilization began in 509 B.C. and ended in 476 A.D. How long did Roman Civilization last?

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?

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?

The temperature at midnight was 2°F. At sunrise, the temperature was 5 degrees lower. What is the temperature?

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?

David and Lisa played a game. David scored -150 points and Lisa scored -450 points. How many points did they score all together?

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:

Factors of 16: 1, 2, 4, 8, 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Greatest Common Factor: 8

Answer:

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

Answer:

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:

The numerator is 37.
The denominator is still 7.

Answer:

The numerator is 111.
The denominator is still11.

Answer:

To change an improper fraction into a mixed number complete the following steps:

Divide the numerator by the denominator.
The number of times the denominator “goes into” the numerator is the whole number.
The remainder is the new numerator.
Keep the denominator the same and simplify if necessary.

Examples:

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:

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:

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

Simplify the following fractions or mixed numbers.

Change each mixed number into an improper fraction.

Change each improper fraction into a mixed number.

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:

Answer:

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

Or, change into an improper fraction →

Answer:

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:

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:

Solve.

Answer:

Find the least common multiple:

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

LCM: 24

Rewrite the fractions:

Solve.

Answer:

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

John walked of a mile yesterday and of a mile today. How many miles has John walked?

Mary is preparing a final exam. She study hours on Friday, hours on Saturday, and hour on Sunday. How many hours did she study over the weekend?

A recipe requires teaspoon cayenne pepper, teaspoon black pepper, and teaspoon red pepper. How much pepper does this recipe need?

A football player advances of a yard. A second player in the same team advances yards. How many more yards did the second player advance?

John lives mile from the Museum of Science. Sylvia lives mile from the Museum of Science. How much closer is Sylvia from the museum?

Ted used the amounts of spices listed below to make a pie.

2 teaspoons of cinnamon

teaspoon of nutmeg

teaspoon of cloves

What is the total number of teaspoons of spices that Ted used?

A recipe needs teaspoon black pepper and red pepper. How much more black pepper does the recipe need?

Amy usedcans of chicken broth to make soup. Each can contained ounces of broth.What was the total number of ounces of chicken broth that Amy used?

A carpenter cuts a board that is feet long. After the cut, feet remain. How long was the piece that was cut?

Bill and Andy were racing to see who could run the farthest in 5 minutes. Bill ran of a mile, and Andy ran of a mile. How much farther did Andy run than Bill?