Download Topic: Integers

Topic: Integers
Examples:
Addition
Same signs:
Add & keep sign
+6 + +5 = +11
-8 + -2 = -10
Subtraction
Keep–Change-Opposite
+10
-5
Different signs:
Subtract & take sign of
larger value
+9 + -5 = +4
-6 + +1 = -5
Multiplication
- -8 = +10 + +8 = 18
Division
Same signs:
Positive product
(+7) (+8) = +56
(-2) (-6) = +12
Same signs:
Positive quotient
+42 / +6 = +7
-24 / -8 = +3
Different signs:
Negative product
(+3) (-9) = -27
(-5) (+4) = -20
Different signs:
Negative quotient
+56 / -7 = - 8
-50 / +2 = - 25
– +12 = -5 + -12
-20
- -8 = -20 + -8 = -12
Recall the order of operations:
1 – Parentheses (or grouping symbols)
2 - Exponents
3 - Multiplication / Division (left to right)
4 - Addition/Subtraction (left to right)
Find each answer.
1. -12 + (-7) = ____
Answers:
2. -25 + 18 = ____
1. ___________
2. ___________
3. 2 + (-25) = ____
4. -28 - (-8) = _____
3. ___________
4. ___________
5. 11 - (-5) = ____
6. -21 - 4 = ____
5. ___________
6. ___________
-
-
7. ( 9)( 8) = _____
-
8. (2)( 12) = _____
7. ___________
8. ___________
9. - 35 / - 7 = _____
10. - 48 / + 8 = _____
9. ___________
10. __________
11. ( - 2)( + 6)(- 5) = _____
12. -30
24
( 2) = _____
6
11. __________
12. __________
13. __________
13.
1
16
2 ( 8) = _____
4
14. -3(1 – 8) + 23 = _____
14. __________
Topic: Rationals
page 4
Multiplying Fractions and Mixed Numbers
1) Change any mixed numbers to improper fractions
2) Cross – cancel any numerator with any denominator by dividing each by a common factor
3) Multiply numerator by numerator and denominator by denominator
4) Simplify your answer (make it a mixed number if you can)
Dividing Fractions and Mixed Numbers
1) Change any mixed numbers to improper fractions
2) Remember Keep-Change-Flip: keep the first fraction, change the division sign to a multiplication
sign, and flip the second fraction
3) Multiply numerator by numerator and denominator by denominator
4) Simplify your answer (make it a mixed number if you can)
Adding and Subtracting Fractions and Mixed Numbers
1) Check to see if the denominators are the same; if not, find a common denominator
2) Now add or subtract the fractions – remember, keep the denominator!
3) Add or subtract the whole numbers
4) Simplify the fraction
5) Rewrite the sum or difference
1) 3 23
5 14
2) 8 54 3 23
2
2 12
3) 5 11
Answers:
1. ___________
2. ___________
4) 12 4 53
5)
2 13 5 34
6)
5 56 12 83
3. ___________
4. ___________
5. ___________
7) 3 13 7 12
8)
3 15
5
6
9)
6 23
3 34
6. ___________
7. ___________
8. ___________
9. ___________
2
Topic: Combining Like Terms and Applying the Distributive Property
In algebraic expressions, like terms are terms that contain the same variables raised to the same power.
Only the coefficients of like terms may be different.
In order to combine like terms, we add or subtract the numerical coefficients
of the like terms using the Distributive Property: ax + bx = (a + b)x .
Examples:
1. 2x + 9x = (2 + 9) x = 11x
2. 12y - 7y = (12 – 7) y = 5y
3. 5x + 8 - 2x + 7 = 3x + 15
Here, the like terms are: 5x and -2x = 3x
and: 8 + 7 = 15
The Distributive Property of multiplication over addition/subtraction is frequently used in Algebra:
Examples:
1. 7 (2x + 9) = 7 2x + 7 9 = 14x + 63
2. 4 (6 – 5x) = 4 (6) - 4(5x) = 24 - 20x
Simplify each expression by combining like terms.
Answers:
1. 8y + 2y
1. ______________
2. 10 – 6y + 4y + 9 =
2. ______________
3. 3x + 7 – 2x =
3. ______________
4. 8n – 7y – 12n + 5 – 3y =
4. ______________
Apply the distributive property and write your answer in simplest form.
3
5. 7(x – 4) =
5. ______________
6. 5(4n – 3) =
6. ______________
7. -6(3y + 5) =
7. ______________
8. -4(8 – 9x) =
8. ______________
9. 8(3n + 7) – 10n =
9. ______________
10. – 4(5 + 7y) + 6(2y – 9) =
10. ______________
Topic: Algebra
Solving equations by using the Addition, Subtraction or Multiplication Property of Equality.
Check the solution.
1
x
2
Ex 1:
5
5
2 1
x
1 2
Check:
5
7x
8
1
x
2
5
6
4x
4 2
x
1 8
( )
2 1
Ex 2: 7x – 6 - 11x = –14
9
11 x
6
14
14
+ 6 +6
4x
8
4
4
x = 2
9
5
9
4 + 5 = 9
9= 9
Check:
7x - 6 - 11x = - 14
7(2) - 6 -11(2) = -14
14 - 6 - 22 = -14
8 - 22 = -14
-14 = -14
Translate and evaluate the following equations.
Ex 3: The product of 4 and a number is 28.
Example: 2
4 n
4n
4
n
28
28
4
7
Ex 4. The quotient of a number
and 3 is 15.
n
3
n
Addition: sum, more than
Multiplication: product
15
45
Subtraction: difference, less than
Division: quotient
Information: Hints, topics, definitions. Any kind of helpful information.
Solve the following equations. Show your work and check your solution.
1. 2 x
Check:
4
5
17
2. 1 x
3
Check:
9
12
3. 5x + 8 = - 12
Check:
Apply the distributive property first.
4.
4x
8
32
5.
Check:
x
4
8
20
Check:
6. 2(x – 7) = 8
Check:
Apply the distributive property first.
7. 8x – 5 – 6x = 7
Check:
8. 3 = 4x – 10x + 15
Check:
9. 6x – (3 + 8x) = -11
Check:
Translate each sentence to an algebraic equation. Then use mental math to find the solution.
Equation
5
Solution
10. One-half of a number is -12.
_____________________
_____________
11. 6 more than 7 times a number is 41.
_____________________
_____________
12. 5 less than three times a number is 10.
_____________________
_____________
13. 16 increased by twice a number is – 24.
_____________________
_____________
Topic: Angle Relationships… and Algebra
Notation: m
means the " measure of angle "
means congruent or equal in measure
Vertical Angles
Complementary Angles
Supplementary Angles
1
4
1
2
3
2
Angles that are opposite
each other across two
intersecting lines.
Two angles whose sum
is 90o.
m
m
1 m 3 and
2 m 4
m
1
m
2
1
2
900
Two angles whose sum
is 180o.
m
1
m
2
1800
State how the angle labeled x is related to the angle with the given measurement.
Find the value of x in each figure.
1)
xº
49º
3
1) _________________________
x = ___________
2) _________________________
2)
x = ___________
xº
62º
3)
6
xº
3) _________________________
123º
x = ___________
4) Find the missing angles.
Note: the angles are not drawn to scale.
Given: 4 = 50˚
Find each angle and write your reasoning.
1=
2
3
4
2=
1
3=
5)
5)
Relationship ________________
x = ________________
(11x - 4)°
2
(3x + 10)° →1
7
3
m
1 = ___________
m
2 = ___________
m
3 = ___________
Topic: Geometry
You should know the following formulas and be able to use them to find the area or perimeter of a
geometric figure.
Perimeter of a polygon = the sum of the sides
Rectangle:
Square:
Parallelogram:
Triangle:
Trapezoid:
Circle:
P = 2l + 2w
P = 4s
P = s1 + s2 + s3 + s4
P = s1 + s2 + s3
P = s1 + s2 + s3 + s4
Circumference = πd
A = lw
A = s2
A = bh
A = ½ bh
A = ½ (b1 + b2)h
A = πr2
Find the perimeter/circumference and area of each figure. Express #6 in terms of pi (π).
Show your work. (Use and attach a separate work page if space is needed.)
1.
2.
5 cm
4.5 cm
7 cm
3.
4.
7 ½ in
8 cm
10 cm
5 in
4 in
20 cm
9 in
5.
5 cm
5 cm
4 cm
11 cm
8
6.
5 cm
5 ft
9) Name each figure. Find the volume or surface area of each. (Use the reference sheet at the back!)
a) Name: _________________
Volume: _________________
b) Name: ________________
Surface Area: _______________
(in terms of pi)
12 in.
4 in.
10 in.
10 in.
5 in.
c) Name: _________________
Volume: _________________
d) Name: _________________
Volume: _________________
(in terms of pi)
13 in.
3 in.
9 in.
10) A storage tank shaped like a rectangular prism is being manufactured to hold 100,000 cubic feet of natural
gas. It has a length of 10 feet and a width of 25 feet. Use algebra to find out what height the tank should be.
9
Topic: Ratio & Proprtion
1) Buck drove 220 miles in 5 hours. What was his average rate of speed?
2) Horace read 160 pages in 4 hours. How many pages can he read in 6 hours?
3) Pasha bought 3 pounds of onions for $2.67. Which ratio is proportional to 3 pounds at $2.67?
A.
10
B.
C.
D.
8th Grade – Summer Math Packet
Unit: Knowledge of Algebra, Patterns, and Functions
Objective: Write an algebraic expression to represent unknown quantities with one unknown and 1 or 2 operations.
Examples:
The tables below show phrases written as mathematical expressions.
Phrases
9 more than a number
the sum of 9 and a number
a number plus 9
a number increased by 9
the total of x and 9
Phrases
Expression
Phrases
4 subtracted from a number
a number minus 4
4 less than a number
a number decreased by 4
the difference of h and 4
X+9
Expression
6 multiplied by g
6 times a number
the product of g and 6
Phrases
h-4
Expression
a number divided by 5
the quotient of t and 5
divide a number by 5
6g
t
5
Write each phrase as an algebraic expression.
1.) 7 less than m
2.) The quotient of 3 and y
3.) 7 years younger than Jessica
4.) 3 times as many marbles as Bob has
5.) Let t = the number of tomatoes Tye planted last year.
This year she planted 3 times as many. Write an
algebraic expression to show how many tomatoes Tye
planted this year.
6.) Last week Jason sold x number of hot dogs at the
football game. This week he sold twice as many as last
week, and then he sold 10 more. Write an expression to
show how many hot dogs Jason sold this week.
3
11
Expression
8th Grade – Summer Math Packet
Unit: Knowledge of Algebra, Patterns, and Functions
Objective: Evaluate an algebraic expression using one unknown and no more than 2 operations.
Example 1: Evaluate 6x – 7 if x = 8.
6x – 7 = 6(8) – 7
= 48 – 7
= 41
Replace x with 8.
Use order of operations.
Subtract 7 from 48.
Example 3: Evaluate
7b
if b = 6.
3
7b (7)(6)
=
3
3
42
=
3
= 14
Example 2: Evaluate 5m – 15 if m = 6.
5m – 15 = 5(6) – 15
= 30 – 15
= 15
Replace m with 6..
Use order of operations.
Subtract 15 from 30.
Example 4: Evaluate x3 + 4 if x = 3.
Replace b with 6.
x3 + 4 = 33 + 4
Replace x with 3.
Multiply 6 by 7.
= 27 + 4
Use order of operations.
Divide.
= 31
Add 27 and 4.
Evaluate the following expressions using the given values for a, b, and c. Show each step!
1.) Evaluate 6 + 3b if b = 7
2.) Evaluate 6a2 if a = 4
3.) Evaluate 5(6) – c if c = 7
5.) Evaluate
4.) Evaluate b4 if b = 2
4
6.) Evaluate (n )2 if n = 9
3
7.5m
if m = 2
5
4
12
8th Grade – Summer Math Packet
Unit: Knowledge of Algebra, Patterns, and Functions
Objective: Evaluate numeric expressions using order of operations with no more than 4 operations.
Use the order of operations to evaluate numerical expressions.
1. Do all operations within grouping symbols first.
2. Evaluate all powers before other operations.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
Example 1: Evaluate 14 + 3(7 – 2) – 2 ! 5
Example 2: 8 + (1 + 5)2 ÷ 4
14 + 3(7 – 2) – 2 ! 5
= 14 + 3(5) – 2 ! 5
= 14 + 15 – 2 ! 5
= 14 + 15 – 10
= 29 – 10
= 19
8 + (1 + 5)2 ÷ 4
= 8 + (6)2 ÷ 4
= 8 + 36 ÷ 4
=8+9
= 17
Subtract first since 7 – 2 is in parentheses
Multiply left to right, 3 ! 5 = 15
Multiply left to right, 2 ! 5 = 10
Add left to right, 14 + 15 = 29
Subtract 10 from 29
Evaluate each of the following. Show each step!
1.) (2 + 10)2 ÷ 4
2.)
(6 + 5) ! (8 – 6)
3.)
4.)
3 ! 14(10 – 8) – 60
72 ÷ 3 – 5(2.8) + 9
5.) The perimeter of a hexagon is found by adding the
lengths of all six sides of the hexagon. For the hexagon
below write a numerical expression to find the perimeter.
Then evaluate the expression.
6.) Without parentheses, the expression 8 + 30 ÷ 2 + 4
equals 27. Place parentheses in the expression
so that it equals 13; then 23.
5
13
Add first since 1 + 5 is in parentheses
Find the value of 62
Divide 36 by 4
Add 8 and 9
8th Grade – Summer Math Packet
Unit: Knowledge of Algebra, Patterns, and Functions
Objective: Determine the unknown in a linear equation with 1 or 2 operations
Remember, equations must always remain balanced.
• If you add or subtract the same number from each side of an equation, the two sides remain equal.
• If you multiply or divide the same number from each side of an equation, the two sides remain equal.
Example 1: Solve x + 5 = 11
x + 5 = 11 Write the equation
-5 =-5
Subtract 5 from both sides
x = 6
Simplify
Example 2: Solve - 21 = - 3y
- 21 = - 3y Write the equation
- 3 = - 3 Divide each side by – 3
7 = y
Simplify
Example 3: Solve 3x + 2 = 23
3x + 2 = 23 Write the equation
- 2 = - 2 Subtract 2 from each side
3x = 21 Simplify
3
3 Divide each side by 3
x = 7 Simplify
Check
x + 5 = 11 Write the equation
6 + 5 = 11 Replace x with 6
11 = 11!
! The sentence is true
Check
- 21 = - 3y Write the equation
- 21 = - 3(7) Replace the y with 7
-21 = - 21? Multiply – is the sentence true?
Check
1.) Solve x – 9 = -12
2.) Solve 48 = - 6r
3.) Solve 2t + 7 = -1
4.) Solve 4t + 3.5 = 12.5
5.) It costs $12 to attend a golf clinic with a local pro.
Buckets of balls for practice during the clinic cost $3 each.
How many buckets can you buy at the clinic if you have
$30 to spend?
6.) An online retailer charges $6.99 plus $0.55 per pound
to ship electronics purchases. How many pounds is a DVD
player for which the shipping charge is $11.94?
8
14
3x + 2 = 23 Write the equation
3(7) + 2 = 23? Replace x with 7
21 + 2 = 23? Multiply
23 = 23? Add – is the sentence true?
8th Grade – Summer Math Packet
Unit: Knowledge of Algebra, Patterns, and Functions
Objective: Graph rational numbers on a number line.
Rational Numbers are numbers that can be written as fractions.
Some examples of rational numbers are ½ , 5 ¾ , 0.8, and -1.4444…
Example: Graph and label the following numbers on the number line:
A:
1
2
B: 4
1
4
C: - 4.5 D: 2.5
1.) Graph and label the following numbers on the
number line.
C
A
D
B
"
"
"
"
2.) Graph and label the following numbers on the
number line.
A: –5 B: –1 C: 2 D: 5
A: 0 B: –1
3.) Graph and label the following numbers on the
number line.
A: –
5.) Jonah recorded the temperature for 5 days on a chart.
Draw a number line and graph the temperatures. Where
do the numbers on the line need to begin and end? Label
the points 1 to 5.
Day 2
50°
Day 3
53°
Day 4
57°
5
2
D: 4
9
3
B: –
3
2
C:
9
4
D:
12
3
6.) Graphing numbers on a number line can help you put
them in order from smallest to greatest. Draw a number
line and graph the numbers in the chart below. Label the
points. Which number is the smallest?
Day 5
60°
V
20
12
15
C:
4.) Graph and label the following numbers on the
number line.
A: 1.5 B: –0.5 C: –3.5 D: 3.5
Day 1
45°
1
2
W
–10
X
–15
Y
5
Z
10
8th Grade – Summer Math Packet
Unit: Knowledge of Algebra, Patterns, and Functions
Objective: Graph ordered pairs in a coordinate plane.
The coordinate plane is used to locate points. The horizontal number line is the x-axis. The vertical
number line is the y-axis. Their intersection is the origin.
Points are located using ordered pairs. The first number in an ordered pair is the x-coordinate; the
second number is the y-coordinate.
The coordinate plane is separated into four sections called quadrants.
Example 1: Name the ordered pair for point P. Then identify the quadrant in which P lies.
• Start at the origin.
Quadrant 2
• Move 4 units left along the x-axis.
• Move 3 units up on the y-axis.
The ordered pair for point P is (- 4, 3).
P is in the upper left quadrant or quadrant II.
Example 2: Graph and label the point M (0, - 4).
• Start at the origin.
• Move 0 units along the x-axis.
• Move 4 units down on the y-axis.
• Draw a dot and label it M(0, - 4).
Quadrant 3
1.) Name the ordered pair for each point graphed at the
right. Then identify the quadrant in which each point lies.
Coordinates
Quadrant 4
2.) Find each of the points below on the coordinate plane.
Then identify the quadrant in which each point lies.
Coordinates
Quadrant
Quadrant
P (___, ___)
____
A (___, ___)
____
Q (___, ___)
____
J (___, ___)
____
R (___, ___)
____
B (___, ___)
____
S (___, ___)
____
H (___, ___)
____
3.) Graph and label each point on the coordinate plane.
4.) Graph and label each point on the coordinate plane.
N
(3, -1)
D
(0, 4)
P
(-2, 4)
E
(5, 5)
Q
(-3, -4)
G
(-3, 0)
R
(0, 0)
H
(-6, -2)
S
(-5, 0)
J
(0, -2)
13
16
Quadrant 1
8th Grade – Summer Math Packet
Unit: Knowledge of Geometry
Objective: Determine the congruent parts of polygons.
Congruent Polygons
Non Congruent Polygons
Polygons that have exactly the same size and
the same shape
Segments that have the same length
Angles that have the same measure
Sides of a polygon that are matched up with
sides of another congruent or similar polygon
Angles of a polygon that match up with angles
of another congruent or similar polygon
Corresponding sides and angles of congruent
polygons are congruent:
Congruent Polygons
Congruent Segments
Congruent Angles
Corresponding Sides of a Polygon
Corresponding Angles of a Polygon
∆ABC ≅ ∆DEF
A
3cm
B
1.)
G
4cm
F
D
3cm
C
7cm
5cm
E
L
H
45°
8cm
J
K
AB ≅ DE
BC ≅ EF
AC ≅ DF
F
7cm
y
2.) Use the figures in problem #1 to complete the following
congruence statements.
M
x
z
8cm
N
Polygon FGHJ ≅ polygon NMLK
Complete the following congruence statements.
GH ≅ _____
KL ≅ _____
y = ______
∠K ≅ _____
∠H ≅ _____
∠F ≅ _____
4.) Polygon HJKLMNPQ is congruent to polygon
RSTUVXYZ. What is the length, in units, of RZ?
(Note: Figures are not drawn to scale.)
z = ______
19
17
∠G ≅ _____
IJ ≅ _____
3.) Look at the figures in problem #1. Determine the
measure of each segment or angle.
x = ______
∠A ≅ ∠D
∠B ≅ ∠E
∠C ≅ ∠F
8th Grade – Summer Math Packet
Unit: Knowledge of Number Relationships & Computation
Objective: Determine equivalent forms of rational numbers expressed as fractions, decimals, percents, and ratios. - A
Examples:
To write a decimal as a fraction, divide the numerator of the fraction by the denominator.
Use a power of ten in the denominator to change a decimal to a fraction.
Write
5
as a decimal.
9
0.555
9 5.000 = 0.5 because 5 repeats forever.
- 45
50
- 45
50
- 45
Write 0.32 as a fraction in simplest form.
0.32 =
1.) Write 0.735353535… using bar notation to represent
the repeating decimal.
3.) Write 4
5
as a decimal.
8
5.) Write 0.48 as a fraction in simplest form.
32
÷4 8
=
=
100 ÷ 4 25
2.) Write
4.) Write 0.94 as a fraction in simplest form.
6.) There were 6 girls and 18 boys in Mrs. Johnson’s math
class. Write a ratio of the # of girls to the # of boys in
fraction form. Then write the fraction as a repeating
decimal.
38
18
3
as a decimal.
5
8th Grade – Summer Math Packet
Unit: Knowledge of Number Relationships & Computation
Objective: Determine equivalent forms of rational numbers expressed as fractions, decimals, percents, and ratios.- B
Examples:
A RATIO is a comparison of two numbers by division. When a ratio compares a number to 100, it can be
written as a PERCENT. To write a ratio or fraction as a percent, find an equivalent fraction with a denominator
of 100. You can also use the meaning of percent to change percents to fractions.
Write
19
as a percent.
20
19 • 5 95
=
= 95% Since 100 ÷ 20 = 5, multiply the numerator and denominator by 5.
20 • 5 100
Write 92% as a fraction in simplest form.
92 ÷ 4 23
=
=
100 ÷ 4 25
Write 92% as a decimal.
Move decimal two places to the left. Add zeros if needed.
92.0% = 0.92
Write 0.4 as a percent.
Move decimal two places to the right. Add zeros if needed.
0.4 = 40%
1.) Write
7
as a percent and decimal.
25
2.) Write 19% as a decimal and fraction in simplest form.
3.) Write
9
as a percent and decimal.
50
4.) Write 75% as a decimal and fraction in simplest form.
5.) Ms. Crest surveyed her class and found that 15 out of
30 students brushed their teeth more than twice a day.
Write this ratio as a fraction in simplest form, then write it
as a % and a decimal.
6.) A local retail store was having a sale and offered all
their merchandise as a 25% discount. Write this percent
as a fraction in simplest form, then write it as a decimal.
39
19
8th Grade – Summer Math Packet
Unit: Knowledge of Number Relationships & Computation
Objective: Compare, order, and describe rational numbers.
Examples:
•
RATIONAL numbers include fractions, decimal, and percents. To COMPARE or ORDER rational
numbers, they must be in the same form (all fraction or all decimals, or all %s)
Example: Order 0.6, 48%, and
1
from least to greatest.
2
Step 1 – Change all to decimals.
Step 2 – Compare decimals & Order.
Step 3 – Write using original form.
0.6
48% = 0.48
0.48, 0.5, 0.6
48%,
1
, 0.6
2
1.) Order from least to greatest.
22%, 0.3,
1
= 0.5
2
2.) Order from least to greatest.
1
5
0.74,
3
, 70%
4
4.) Which is the largest?
3.) Replace
with <, > , or =.
1
7
12
1
3
10
1
4
9
58%
5.) According to the Pet Food Manufacturer’s Association,
11 out of 25 people own large dogs and 13 out of 50
medium dogs. Do more people own large or medium
dogs?
6.) Your PE teacher asked you to run for specific time
period. You ran 0.6 of the time. Two of your friends ran
7
and 72% of the time. Order the amount of time you
10
and your friends ran from least to greatest.
40
20
3
8
8th Grade – Summer Math Packet
Unit: Knowledge of Number Relationships & Computation
Objective: Add, subtract, multiply and divide integers. - A
Examples:
ADDITION INTEGER RULES:
For integers with the same sign:
• The sum of two positive integers is POSITIVE.
• The sum of two negative integers is NEGATIVE.
For integers with different signs, subtract their absolute value. The sum is:
• Positive IF the positive integer has the greater absolute value.
• Negative IF the negative integers has the greater absolute value.
Examples:
- 6 + (- 3) = add keep the sign = - 9
- 34 + (- 21) = add keep the sign = - 55
8 + (- 7) = subtract keep the sign of the higher = 1
- 5 + 4 = subtract keep the sign of the higher = - 1
SUBTRACTION INTEGER RULES:
• Keep the first number the same
• Switch the subtraction sign to ADDITION
• Change the second number to it’s opposite. Opposite: - 6 to 6
• Follow Addition rules above.
Examples:
6 – 9 = 6 + (- 9) = -3
- 3 – 7 = - 3 + (- 7) = - 10
- 10 – (- 12) = - 10 + 12 = 2
1 – ( - 2) = 1 + 2 = 3
1.) Add: 2 + (- 7)
2.) Subtract: - 13 - 8
3.) Evaluate a – b if a = - 2 and b = - 7
4.) Evaluate x + y + z if x = 3, y = - 5, and z = - 2
5.) In Mongolia the temperature can dip down to – 45o C
in January. The temperature in July may reach 40o C.
What is the temperature range in Mongolia?
6.) Write an addition expression to describe skateboarding
situation. Then determine the sum.
Hank starts at the bottom of a half pipe 6 feet below street
level. He rises 14 feet at the top of his kickturn.
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8th Grade – Summer Math Packet
Unit: Knowledge of Number Relationships & Computation
Objective: Add, subtract, multiply and divide integers. - B
Examples:
MULTIPLYING & DIVIDING INTEGER RULES:
• Two integers with DIFFERENT signs the answer is NEGATIVE.
• Two integers with SAME signs the answer is POSITIVE.
Examples:
5 (- 2) = 5 times – 2, the signs are different so the answer will be negative = - 10
(- 6) • (- 9) = the signs are the same so the answer will be positive = 54
30 ÷ (- 5) = the signs are different so the answer will be negative = - 6
- 100 ÷ (- 5) = the signs are the same so the answer will be positive = 20
1.) Mulitply:
- 14 (- 7)
2.) Divide: 350 ÷ (- 25)
3.) Evaluate if a = - 3 and c = 5
4.) Evaluate if d = - 24, e = - 4, and f = 8
- 3ac
5.) A computer stock decreased 2 points each hour for 6
hours. Determine the total change in the stock value over
the 6 hours.
de
f
6.) A submarine descends at a rate of 60 feet each
minute. How long will it take it to descend to a depth of
660 feet below the surface?
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22
8th Grade – Summer Math Packet
Unit: Knowledge of Number Relationships & Computation
Objective: Add, subtract, and multiply positive fractions and mixed numbers. - A
Examples:
• To add unlike fractions (fractions with different denominators), rename the fractions so there is a
common denominator.
1 2
+ =
6 5
Add:
1
2
Add: 12 + 8 =
2
3
3
4
7
12 + 8 = 20
6
6
6
20 + 1
1.) Add:
1 1x5
5
=
=
6 6 x5 30
12
2 2 x6 12
=
=
5 5 x6 30
1
1x3
3
= 12
= 12
2
2 x3
6
8
2
2 x2
4
=8
=8
3
3x2
6
7
1
is improper so we must change it to proper. 7 divided by 6 = 1
6
6
1
1
= 21
6
6
1 1
+
3 9
2.) Add:
4
2
7 + 10
9
9
5
1
3.) Add: 1 + 4
9
6
1
2
4.) Add: 2 + 2
2
3
3
cups of grated cheese.
4
1
A recipe for quesadillas requires 1 cups of grated
3
cheese. What is the total amount of grated cheese
needed for both recipes?
6.) You want to make a scarf and matching hat. The
7
pattern calls for 1 yards of fabric for the scarf and
8
1
2 yards of fabric for the hat. How much fabric do you
2
need in all?
5.) A quiche recipe calls for 2
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23
5 12 17
+
=
30 30 30
*** Mathematical websites that would be most helpful are:
- www.khanacademy.org
- www.learnzillion.com
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