Download adding integers - Colts Neck Township Schools

June 2014
Dear Parents/Guardians:
As your child’s 7th grade school year comes to an end, thoughts of sleeping late
and spending time with friends are, no doubt, on the mind. We hope your child
will have a fun-filled and relaxing summer. We also hope he or she will spend just
a little time reviewing and maintaining the math skills acquired during this past
school year.
To ensure that your child has a successful start to their eighth grade math class,
we have prepared a Summer Math Packet that we encourage each child entering
eighth grade math to complete. All objectives included in the assignment have
been taught and reinforced during 6th and/or 7th grade. We have found that by
encouraging students to complete the packet over the summer, we are able to
spend less time at the beginning of the year reviewing prior knowledge and more
time introducing new concepts. With this in mind, please encourage your child to
work on the assignment throughout the summer.
Answer keys are available in the main office.
Thank you and have a wonderful summer!
Ms. Rupinski & Ms. Jaeger
Prime Factorization
Using a factor tree, find the prime factorization for each of the following numbers.
Then, rewrite the prime factorization using exponents.
1.
36
2.
48
3.
17
4.
50
5.
96
6.
40
Greatest Common Factor
1) List the factors for each of the following numbers:
18____________________________________________________________
24____________________________________________________________
What factors do 18 and 24 have in
common?__________________________
What is the greatest common factor of 18 and
24?______________________
2) List the factors for each of the following numbers:
30______________________________________________________________
56______________________________________________________________
What factors do 30 and 56 have in
common?____________________________
What is the greatest common factor of 30 and
56?________________________
Find the greatest common factor for each set of numbers below.
3)
45 and 12
4)
10 and 16
5)
19 and 30
6)
34 and 17
7)
42 and 7
8)
12 and 27
Least Common Multiple
1) List the first 12 multiples for each of the following numbers:
8____________________________________________________________
3____________________________________________________________
What multiples do 8 and 3 have in
common?__________________________
What is the least common multiple of 8 and
3?______________________
2) List the first 12 multiples for each of the following numbers:
4______________________________________________________________
12______________________________________________________________
What multiples do 4 and 12 have in
common?____________________________
What is the least common multiple of 4 and
12?________________________
Find the least common multiples for each set of numbers below.
3)
8 and 10
4)
12 and 15
5)
7 and 9
6)
16 and 48
7)
20 and 25
8)
10 and 16
COMPARING & ORDERING INTEGERS
You can use a number line to order integers. On a number line, a number to the
left is less than a number to the right.
Replace each
1.
O
–5
with < or > to make a true sentence.
2.
O
17 O -18
-6
3.
4.
–45
O
-43
5.
15
O
-2
6.
–19
O
–16 O -28
21
Order the integers from least to greatest.
1. 8, -3, 6, -4, 5
2.
17, 12, -14, -6, 5, -3, -2
3. –7, 8, -11, 14, 16, -12
4.
0, -5, -2, 3, 8, 10, -16
INTEGERS & ABSOLUTE VALUE
An integer is any number from the set ..., 3,2,1,0,1,2,3... . Integers greater than
zero are positive integers. Integers less than zero are negative integers. Zero
is neither positive nor negative.
Write an integer for each situation.
1. to move back three spaces
2. a gain of 15 yards
3. 20F below zero
4. a shirt that shrunk 4 inches
Find the absolute value of each integer.
1. 6
2. –3
3. –4
4. 12
CONVERTING FRACTIONS TO DECIMALS
To convert a fraction to a decimal, divide the numerator of the fraction by the
denominator.
Convert each fraction to a decimal. Round to the nearest tenth, if necessary.
1.
12
25
2.
7
30
3.
245
1000
4.
10
28
5.
28
60
6.
8
120
7.
48
325
8.
101
12
CONVERTING FRACTIONS TO PERCENTS
To convert a fraction to a percent, first divide the numerator of the fraction by the
denominator. Then move the decimal point two places to the right. The new
number is the percent and should be written with the percent symbol, %.
Example: Write 7 as a percent.
10
7 = .70 = 70%
10
Convert each fraction to a percent. Round to the nearest tenth, if necessary.
1.
10
25
2.
9
30
3.
160
1000
4.
12
28
5.
32
60
6.
16
120
7.
54
325
8.
236
12
CONVERTING PERCENTS TO DECIMALS
To convert a percent to a decimal, divide the percent by 100 and remove the
percent symbol.
Example: Write 57% as a decimal.
57% = 0.57
Convert each percent to a decimal.
1.
36%
2.
7%
3.
125%
4.
99.8%
5.
15.1%
6.
11%
7.
.75%
8.
12.30%
ADDING INTEGERS
Evaluate each expression. Do not use a calculator.
1. 8 + 15
2. –7 + 7
3. 8 + (-2)
4. –2 + 3
5. –6 + (-3)
6. –10 + 12
7. –9 + 5
8. –45 + (-22)
9. –32 + 17
10. 26 + (-51)
11. -12 + 24 +(-12) + 2
12. -17 + 5 + 9 + 3
13. 10.4 + (-13.8)
14. -26.4 + 37.2
SUBTRACTING INTEGERS
Evaluate each expression. Do not use a calculator.
1. 6 – (-3)
2. –9 - 4
3. –4 – (-8)
4. –2 – (-1)
5. –12 - 6
6. –10 - 13
7. 9 - 15
8. –45 - 15
9. –32 – (-7)
10. 50 - 75
11. -29 - 29
12. 0 - 52
MULTIPLYING INTEGERS
Evaluate each expression. Do not use a calculator.
1. 8(-3)
2. –9 (5)
3. – 7(-6)
4. –12 (4)
5. 11 (6)
6. –15 (3 2 )
7. –5 (-8)
8. –4 (-2) 2
9. –8(4)
10. –4(-5)
11. 3 (-8) (-10)
12. (-4) (5) (2.5)
DIVIDING INTEGERS
Evaluate each expression. Do not use a calculator.
1. 16  (-2)
2. –8  (-4)
3. – 48  6
4. 32  (-4)
5. -11  (-11)
6. –15  3
7.
9
3
8.
9.
44
 11
10.
54
9
72
9
EVALUATING EXPRESSIONS
When evaluating expressions, replace the variable with the given values.
Evaluate each expression if b = 12.
1. 43 - b
2. 3b + 6
3. b + 25
4. 2b + 8
Evaluate each expression if x = 8, y = 4, and z = 2.
1. x - y
2. yz - x
3. x + y – 2z
4. 3yz
POWERS AND EXPONENTS
When you multiply two or more numbers, each number is called a factor of the
product. When the same factor is repeated, you can use an exponent to simplify
the notation. An exponent tells you how many times a number, called the base,
is used as a factor. A power is a number that is expressed using exponents.
1. Write 14 · 14 · 14 · 14 · 14 in
exponential form.
2. Write d · d · d · d in exponential
form.
3. Write 2 5 as a product.
4. Write x 6 as a product.
5. Evaluate 12³.
6. Evaluate 15².
ORDER OF OPERATIONS
When you evaluate an expression, the order of operations ensures that the
expression always has only one value. The order of operations tells you which
operation to use first.
Evaluate each expression.
1.
42 2  3
2.
(10 + 12)  11
3.
54  6 + 2 4
4.
7² – (2  3)
5.
3³  2 + 64  4²
6.
9 – 2³  4
7. 3[15 – (2 + 7)  3]
8. -15  3 + (-8 -22 )
ONE-STEP EQUATIONS
In mathematics, an equation is a sentence that contains an equal sign, =. You
solve the equation when you replace the variable with a number that makes the
equation true. To solve a one step equation, you must use the inverse
operation to isolate the variable.
Solve each equation.
1.
a + 5 = 11
2.
22 = j – 2
3.
b – 10 = 2
4.
f = 12
6
5.
3g = 36
6.
g = 15
2
7.
49 = -7x
8.
x + 15 = -15
TWO-STEP EQUATIONS
Solve each equation. Check your solution.
1.
2x + 10 = 22
3.
18 = 4x - 6
5.
6 – 3x = 21
7.
5 – 2n = -1
2.
3x – 9 = -18
4.
-4 =
6.
x
- 2 = 18
3
8.
x + 10 – 3x = 26
1
x+2
3
DISTRIBUTIVE PROPERTY & COMBINING LIKE
TERMS
Using the Distributive Property and combining like terms, simplify each
expression.
1.
-8(x + 5)
2.
7( x – 4)
3.
-6 ( 2n – 7)
4.
3(x – 4) + 12x - 8
5.
3 (2y + 1)
6.
-4(3x + 5)
7.
-3d + 8 – d - 2
8.
5(2x + 4) + 3(-4x – 8)
SOLVING EQUATIONS WITH VARIABLES ON
BOTH SIDES
Solve each equation. Check your solution.
1.
6n – 1 = 4n - 5
2.
7x + 4 = 9x
3.
3 – 10x = 2x - 9
4.
-6x + 13 = 2x - 11
5.
m – 18 = 3m
6.
7k + 12 = 8 – 9k
7.
13.4x + 17 = 5x - 4
8.
½x–3=7–¾x
LINEAR EQUATIONS & SLOPE
Determine whether the following points lie on the graph of y = 3x – 4.
a.
(1, -1)
b.
(2, 2)
c.
(4, 9)
Write an equation for the graph to the right.
Graph the following equations.
y=2x +4
y= -4x - 2
y=½x–3
y=5
Find the slope and y-intecept for each table. Then write an equation.
1.
x
0
1
2
3
4
y
4
9
14
19
24
x
-1
0
1
2
3
y
8
5
2
-1
-4
x
-2
0
2
4
6
y
-5
1
7
13
19
x
1
2
3
4
5
y
-4
-4
-4
-4
-4
x
-2
0
3
4
7
y
4
8
14
16
22
x
-4
-2
-0
2
4
y
7
6
5
4
3
2.
3.
4.
5.
6.