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Full Name : ____________________________________ (the one that will be in Synergy First and Last)

6th grade Math teacher: ____________________ Circle your class: Math 6 Adv Math 6 Math 6/7

Seventh Grade

Summer 2019 Math Packet

o This packet is designed to help you retain previously learned information, so

that you will get off to a great start in seventh grade.

o We have provided notes and examples to get you started.

o Please complete as much of the packet as possible using your knowledge

and our notes and examples.

o This assignment can be turned in on AUGUST 1st for 10 bonus points.

o It is due on AUGUST 14th for everyone.

o In seventh grade, we expect all students to show their work. Credit will not

be given if there is no work.

o Please do NOT use a calculator.

Parent Signature: _____________________

Date Completed: ______________

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Operations with Decimals

ADDITION

To add or subtract decimals, line up the numbers by place value or by the decimal. Then add or subtract as usual.

Whole numbers end in an understood decimal, so 4 can be 4.0!

45.67 + 0.3 + 400.3 =

45.67

.30

+ 400.30

446.27

13.54 + 9 + 4.87 =

13.54

9.00

+ 4.87

27.41

SUBTRACITON To add or subtract decimals, line up the numbers by place value or by the decimal. Then add or subtract as usual.

Use zeroes to fill in empty place values.

76.33 – 3.2 =

76.33

- 3.20

73.13

60.4 – 15.24 =

5 10 3 10

60.40

- 15.24

45.16

MULTIPLICATION

To multiply numbers with decimals, you do not need to line up the decimals. Multiply the numbers, then count how many digits are to the right of the decimals in the problem. Move the decimal in the solution so there are the same number of digits behind the decimal in the solution.

3.12 × 0.5 =

3.12 2 digits behind the decimal

× 0.5 1 digit behind the decimal

1.560 3 total digits behind the decimal

1.56

56 • 0.09 =

56 no digits behind the decimal

• .09 2 digits behind the decimal

5.04 2 total digits behind the decimal

5.04

DIVISION

To divide numbers with decimals, the divisor must be made into a whole number. Move the decimal, in the number that you are dividing by, to the right until it is a whole number. Move the decimal in the dividend, the number you are dividing, the same number of times. Add zeroes if necessary. Divide and move the new decimal up into your solution.

21.84 ÷ 4.2 =

5.2

4.2 )21.84 42) 218.4

- 210

8 4

- 84

0

5.2

34.095 ÷. 05

630

.09)56.7 9) 5670

fill in the blank with a zero - 54

27

-27

0 0

630 - 0 0

0

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Operations with Decimals: YOUR TURN. Do not use a calculator. Show all work

1) 50.48 + 17.83 = 2) 193.4 – 16.97 = 3) 0.07 + 12.4 + 36 =

4) 653 – 7.47 = 5) 74.8 × 7.5 = 6) .03 • .07 =

7) 0.83 × 12 = 8) 50.28 ÷ .3 = 9) 7.95 ÷ 5 =

10) 6.251 ÷ .07 = 11) Add forty-eight and sixty-three hundredths to three and seven hundredths.

12) Subtract four and seven tenths from eleven and ninety-three hundredths.

13) Multiply eight and twenty-four hundredths by six and seven tenths.

14) Divide forty-two and forty-eight hundredths by two tenths.

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Operations with Fractions ADDITION /SUBTRACTION

1- You need a common denominator. 2- Find the least common denominator and make equivalent fractions by multiplying the numerator and denominator by the SAME number. 3- Add or subtract the numerators. Keep the denominator. 4- Simplify if possible.

 1 5

 +    +    3 6

3=  

8

7 3 6 - 4 =

12 8

MULTIPLICATION

1- You do NOT need a common denominator. 2- Change mixed numbers into improper fractions. Multiply the denominator by the whole number and add the numerator.

3- You can cross-simplify any numerator with any denominator. 4- Multiply the numerators, then the denominators. 5- Simplify if possible.

3 4 × =

8

1 3 3 × 2 =

5 4

DIVISION

1- You do NOT need a common denominator. 2- Change mixed numbers into improper fractions. 3- You cannot divide fractions. Instead use the rule of KEEP, CHANGE, RECIPROCAL Keep the first fraction the same. Change the operation to multiply. Use the reciprocal of the second fraction.

4- Use steps for MULTIPLICATION.

3 ÷ 5 = 4

1 2 5 ÷ 4 =

4 3

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Operations with Fractions: YOUR TURN Do not use a calculator. Show all work

7 11) + =

8 4 1 4

2) 3 + 2 =4 5

7 33) 9 + =

8 4

5 34) - =

6 4 5 1

5) 4 - 1 =6 2

1 56) 6 - 3 =

3 6

97) 6 - =

10

4 28) =

9 3

29) 2 3 =

5

4 1

10) 2 1 =5 7

3 1

11) 3 2 =4 3

1

12) 5 =3

7 2

13) =9 3

1 1

14) 3 1 = 3 2

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Order of Operations Order of Operation problems contain numbers and operations.

These problems will NOT contain variable, like x or y.

There are only 4 steps, so we are moving away from PEMDAS.

PEMDAS confuses people, because the acronym has 6 letters…which makes

them think that there are 6 steps.

G: Grouping Symbols

parenthesis, brackets, braces, long division bars that hold some numbers in the numerator and others in the denominator

9 + 2 • 8 – (52-38) ÷ 7 + 53 + 90 ÷ (5 • 6)

9 + 2 • 8 – 14 ÷ 7 + 53 + 90 ÷ 30

E: Exponents

The small superscript numbers written to the upper right of a number that tells us to multiply the base number by itself a certain number of times

9 + 2 • 8 – 14 ÷ 7 + 53 + 90 ÷ 30

53 means 5 • 5 • 5 = 125

9 + 2 • 8 – 14 ÷ 7 + 125 + 90 ÷ 30

M: Multiply and Divide

Do these operations from right to left.

9 + 2 • 8 – 14 ÷ 7 + 125 + 90 ÷ 30

9 + 16 – 2 + 125 + 3

S: Subtract and Add

Do these operations from right to left.

9 + 16 – 2 + 125 + 3

25 – 2 + 125 + 3

23 + 125 + 3

148 + 3

151

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Order of Operations : YOUR TURN Do not use a calculator. Show all work

1) 8 + 9 – 3 + 5 2) 7 • 5 + 2 • 3 3) (84 ÷ 4) ÷ 3

4) 67 + 84 – 12 • 4 5) (9 + 4)(8 - 7) 6) (15 + 21) ÷ 3

7) (38 – 12) ÷ 4 - 3 8) 5 • 6 – 25 ÷ 5 -2 9)

18 + 66

35 - 14

10) 1 + 6 • 3 ÷ 9 • 2 11) 23 - 7 + 14 = 12) 2(5 + 4) – 32 • 2

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Algebraic Expressions Algebra problems contain numbers, operations, and variables, like x and y.

Expressions will have only one side.

Evaluating algebraic expressions:

You can only solve an algebraic expression if you are given the values for the variables.

Substitute and solve. Using order of operations. **a number next to a variable means multiply**

Evaluate the expression if m = 6, n = 0 and p = 2

7p – 9n + 3m

7(2) – 9(0) + 3(6) multiply

14 – 0 + 18 then add and subtract

left to right 14 + 18

32

Simplifying algebraic expression

If you are NOT given the values for each variable, you can only simplify the expression.

1- Distribute. If there is a set of

parenthesis with a number outside, multiply that number by each term inside the parenthesis

2- Combine like terms. Use the

commutative and associative properties to add or subtract the terms that have the same variables.

Simplifying the expression. 7h – 9k + 4(3j + 5k) – 3h 4(3j) = 12j

Distribute 4(5k) = 20k

7h – 9k + 12j + 20k – 3h

Commute, move +/- with the #

7h – 3h + 12j + 20k - 9k Associate, group

4h + 12j + 11k

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Evaluate Algebraic Expressions : YOUR TURN

Evaluate each expression if x = 3, y = 4, and z= 5.

1) 6x – 3y 2) y – x z – y

3) 14x – (2y + z)

4) 2x + 3z + y 5) x(y + z - 2) 6) 4z + 2y 7

Simplify Algebraic Expressions : YOUR TURN

7) 6x + 3y + 6x – 2y 8) 5(w + 2v) + 6w 9) m + 3m + 8

10) 5a + 2c – 2a + 6c 11) 18 + 7x – 12 + 5x 12) 12h + 3+ 18 – 9h

13) 10k – k + 1 14) 3y + 2x + 10x + 7 - 2y 15) 3(f+ 2g) – 11 + 5g + 16

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Algebraic Equations

Algebra problems contain numbers, operations, and variables, like x and y.

Equations will have two sides that are set equal to each other.

The goal is to isolate the variable (get it alone).

To do this, you “undo” whatever is one the side with the variable by doing the

inverse operation on BOTH SIDES of the equation.

INVERSE OPERATIONS:

ADD SUBTRACT MULTIPLY DIVIDE

The inverse of subtract is ADD. z – 5 = 19

+ 5 + 5

z = 24

You can check to see if

you are correct by

substituting the solution

back in

z – 5 = 19

24 – 5 = 19

19 = 19

The inverse of add is SUBTRACT. 42 = g + 11

-11 - 11

31 = g

You can check to see if

you are correct by

substituting the solution

back in

42 = g + 11

42 = 31 + 11

42 = 42

The inverse of multiply is DIVIDE. 8w = 72

÷ 8 ÷ 8

w = 9

You can check to see if

you are correct by

substituting the solution

back in

8w = 72

8(9) = 72

72 = 72

The inverse of divide is MULTIPLY

n

4

= 7

4 • n

4

= 7 • 4

n = 28

You can check to see if

you are correct by

substituting the solution

back in n

4

= 7

28

4 = 7

7 = 7

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Solve and Check Algebraic Equations : YOUR TURN

You need to show what operation you are using to un-do the given operation on BOTH SIDES. Please refer to the notes page.

1) 9 + x = 16 Check 2)

x

6 = 12

Check

3) 6c = 54 4) 12r = 76

5) 18n = 378 6) 32 =

f

8

7) p – 22 = 46 8) m + 15 = 20

9) 5m = 145 10) 7h = 49

11) 98 = 38 + x 12) 100 = 5e

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