6TH GRADE MATH SUMMER INDEPENDENT STUDY
INTRODUCTION:
Welcome to Math at JWJ College Prep! We are so very excited that you are coming to our school! This packet will
help you get prepared for your journey through math. This packet should seem like an easy refresher of elementary
math skills. Hopefully it is nothing new. However, if you find the packet difficult, please do your level best to master
these skills PRIOR to the beginning of 6th grade. It will be instrumental in your success as a 6th grade math student.
OBJECTIVE:
To make sure all students are prepared for a rigorous math environment in middle school
DUE DATES:
This packet is due for completion at the end of the first week of school. It is due for correctness AND you will be
tested on this information during the second week of school. Due to the A day – B day schedule, the actual dates will
be given by your teacher.
ADDITIONAL RESOURCES:
Sometimes a different tutor can help. Here are some great online resources to help you understand any concepts you
are struggling with.
www.mathsisfun.com
www.coolmath.com
www.khanacademy.org
www.softschools.com
www.purplemath.com
www.algebra.com
www.mathscore.com
www.ixl.com
www.mathsteacher.com
www.icoachmath.com
www.onlinemathlearning.com
www.math.tutorvista.com
PRIOR KNOWLEDGE FOR THIS COURSE NOT COVERED IN THIS PACKET:
Students will be expected to have this knowledge prior to entering 6th grade.
 Mastery of long division, showing all arithmetic, without use of a remainder
 Mastery of multiplication and long division involving numbers greater than 100
 Mastery of place value and rounding
 Memorized multiplication tables 1-12 without needing to count
 Mastery of adding, subtracting, multiplying and dividing decimals by whole numbers
 Mastery of adding and subtracting fractions with like denominators and mixed numbers
 Knowledge of common mathematical signs (A dot is used instead of an x to signify multiplication.)
 Mastery of the order of operations
PRIOR KNOWLEDGE FOR THIS COURSE COVERED IN THIS PACKET:
 Decimals- Correctly add, subtract, multiply and divide decimals with decimals.
 Fractions – Correctly add and subtract fractions with unlike denominators, correctly multiply and divide
fractions
EXPECTATIONS:
 Students are not to use a calculator for any portion of this packet.
 Students will show all work and arithmetic on separate paper, numbered by question. These work pages will
be attached to the back of this packet.
 All answers will be neatly and clearly written in the answer spaces provided.
DECIMALS
Adding and Subtracting decimals by other decimals
This skill is very simple. The main rule is to remember to line up the decimals. Even when the place values vary, you
must line up numbers by their decimal points in order to arrive at the correct answer.
ADDING
SUBTRACTING
CORRECT
INCORRECT
CORRECT
INCORRECT
3.1 + 4.25
3.1 + 4.25
4.25 – 1.752
4.25-1.752
3.1
3.1
+4.25
7.35
4.25
+4.25
4.56
4.25
-1.752
- 1.752
0. 673
4.250 When there are spaces above, use zeroes to make
-1.752 the place values even before subtracting.
2.498
PRACTICE: Adding and Subtracting Decimals
# QUESTION
ANSWER
# QUESTION
ANSWER
# QUESTION
ANSWER
1 4.5+6.21
2 9.852+4.25
3 6.45+10.1
4 8.2-4.951
5 9.651-4.2
6 12.92-1.255
Multiplying Decimals by other decimals
This skill requires a superb grip on multiplication. When multiplying decimals by other decimals, you start by
multiplying normally, without paying attention to the decimals. Once done, you count the number of decimal spaces
in both numbers. This is how many decimal places that are used in the answer
EXAMPLE:
4.259
X 2.5
21295
+ 85180
106475
Step 1: Multiply normally
Step 2: Count the decimal places in the numbers being multiplied
4.259 (3 decimal places)
2.5 (1 decimal place)
4 decimal places total
Step 3: Use that many decimal places in your answer.
PRACTICE: Multiplying 2 decimals
# QUESTION
ANSWER
# QUESTION
1 4.5  6.21
2 9.852  4.25
4 8.2  4.951
5 9.6  20.9
ANSWER:
ANSWER
10.6475
#
3
6
QUESTION
6.45  10.1
12.92  1.255
ANSWER
Dividing decimals by other decimals
It is important to note that you cannot divide by a decimal. The divisor must be changed to a whole number prior to
dividing. Therefore, you must move decimal places in the dividend as well.
10
divisor
Must be turned into
a whole number.
2.5 25
quotient (the answer)
dividend
May be a whole number or decimal
When the divisor is a decimal, move the decimal point to the right as many spaces as are needed to create a whole
number.
Important Reminder: If the dividend is a whole number, it is implied that there is a decimal at the end. It
would still move and the blank spaces created would become zeroes.
PRACTICE: Dividing two decimals
# QUESTION
ANSWER
# QUESTION
1 186.25  0.025
2 8.24  0.2
4 45.9  4.59
5 90.2  2.5
ANSWER
#
3
6
QUESTION
24.75  0.33
20.24  2.3
ANSWER
FRACTIONS
These diagrams are from www.helpingwithmath.com
Adding fractions with unlike denominators
You cannot add or subtract two fractions with unlike denominators. First you must change them into like fractions, or
fractions with the same denominator. To do this, you use common multiples.
EAMPLE 1:
1 1

2 3
Once the fractions have the same
denominator, you can add the numerators.
3 2 5
 
6 6 6
EXAMPLE 2:
3 5

4 6
Once the fractions have the same
denominator, you can add the numerators.
9 10 19


12 12 12
EXAMPLE 3:
Simplify to
1
7
12
5 2

7 3
Once the fractions have the same
denominator, you can subtract the
numerators.
15 14 1


21 21 21
PRACTICE: Adding and Subtracting Fractions
Directions: Please remember to simplify all answers
# QUESTION
1 5 6

4
8 16
52 1

60 3
ANSWER
#
2
5
QUESTION
1 11

5 20
1 1

3 6
ANSWER
#
3
6
QUESTION
3 1

8 4
10 4

11 55
ANSWER
Multiplying Fractions
Multiplying fractions is incredibly simple. All you do is multiply the numerators together. Then multiply the
denominators together. No mess. No fuss. Don’t forget to simplify your answer. 
DIVIDING FRACTIONS
This can be a little trickier. You see, you can’t divide fractions as they are. You must multiply by the reciprocal. A
reciprocal is a fraction flipped upside down. The fraction
2
3
has a reciprocal of
.
2
3
How does it work? Well, when you see a question asking you to divide fractions;
1) Change the division sign to a multiplication sign.
2) Use the reciprocal of the second fraction.
3) Multiply across.
4) Simplify as needed.
EXAMPLE
1 3

8 4
STEP 1:
1 3

8 4
STEP 2& 3:
1 4

8 3
=
4
24
Simplified:
1
6
PRACTICE: Multiplying and Dividing Fractions
Directions: Please remember to simplify all answers
# QUESTION
1 7 4
ANSWER

4
8 21
2 4

3 5
#
2
5
QUESTION
ANSWER
5 1

6 2
1 4

5 9
#
3
QUESTION
ANSWER
3 4

10 5
3 2

8 3
6
Multiplying and dividing a fraction by a whole number
This is a lot simpler than it sounds. A whole number is really a fraction in disguise. Every whole number can be placed
as a numerator over 1 without changing the number at all. So 5 can also be written as
5
. Therefore, when multiplying
1
or dividing a fraction by a whole number, just turn the whole number into a fraction, and go with what you know.
EXAMPLE 1:
9
5
12
9 5

12 1
EXAMPLE 2:
Put the whole number over one.
4
6
7
4 6

7 1
Multiply across
9 5 45
 =
12 1 12
4 1
Multiply by the reciprocal

7 6
Simplify
15
4
4
Multiply across
42
2
Simplify
21
PRACTICE: Multiplying ad Dividing Fractions and Whole Numbers
Directions: Please remember to simplify all answers
# QUESTION
1 4
5
4
9
25 
1
5
ANSWER
#
2
5
QUESTION
3
 12
7
3
4
5
ANSWER
#
3
6
QUESTION
3
4
10
2
3
3
ANSWER