Preparing for 7
th
Grade Math
(Enriched)
William Allen Middle School
Moorestown, New Jersey
Preparing for Math 7 Enriched
SHOW ALL WORK – No Calculator
The purpose of the packet is to help you review and reinforce concepts/topics that are
necessary for seventh grade math.
Instructions:
Complete all sections of this packet. You MUST show all work (use additional paper if
necessary). You will return this completed packet to your math teacher during the first
week of school.
This packet will be collected the Friday after Labor Day and
GRADED FOR ACCURACY. All work must be shown and final
solutions should be circled.
You will be tested on the concepts covered in this packet during
the 2
ndweek of school
It may be necessary to seek assistance on some questions/concepts…that is fine!
Websites that may be of assistance:
www.mathforum.org/dr.math
Use this web site if you have a math questions that you
need answered.
www.allmath.com
This website will provide you with links to games, reference, general
math help and resources.
www.mathforum.com
This online community includes teachers, students, researchers,
parents and educators who have an interest in math and math education. The site
includes Ask Dr. Math, Problems of the Week, discussion groups and much more.
www.AAAmath.com
. Customized by grade level and topic, AAA Math features
explanations of various mathematical topics, practice problems and fun, challenging
games.
www.coolmath.com
This fully interactive site and allows the user to sharpen basic math
skills, play games and explore new math concepts.
www.figurethis.org
Created by the National Council of Teachers of Mathematics, this
site helps families enjoy mathematics outside school through a series of fun and
engaging challenges.
Rounding Decimals
Round 24.625 to the nearest tenth
1. Find and underline the place value to which you want to round. 2. Circle the digit to the right of the underlined place value.
3. If the circled number is 5 or above, add one to the underlined place-value. If the circle number is 4 or below, leave the underlined place value alone.
4. Drop all digits to the right of the underlined digit after rounding.
24.625
24.6 2 5
2 is less than 5 so LEAVE IT ALONE!
24.6
1. Write the name of the underlined place value position
2. Round each number to that place value.
1. 46.124
2. 8.0769
3. 0.896
4. 0.334
Adding and Subtracting Decimals
To add or subtract decimals:
1. Line up decimal points to line up correct place-value positions. 2. Insert necessary zeroes.
3. For subtraction, borrow if necessary. 4. Add or subtract.
5. Bring decimal point straight down into answer.
Add or subtract
1. 0.48 + 2.901
2. 0.125 + 0.78
3. 16.354 – 0.27
4. 100.211 + 8.99
5. 75 – 0.24
6. 37.8 – 29.846
Multiplying Decimals
To multiply decimals:1. Line up digits, NOT decimal points. 2. Multiply as with whole numbers.
3. Count the number of decimal places in each factor.
4. The number of decimal places in the product of two decimals is the sum of the number of decimal places in the factors.
Multiply
1. 2 x 0.3
2. 0.4 x 3.8
3. 200 x 0.004
4. 38.3 x 29.1
5. 0.44 x 0.512
6. 34.2 x 80.1
Dividing Decimals
1. Change the divisor to a whole number by moving the decimal point to the right. 2. Move the decimal point in the dividend the same number of places to the right. 3. Divide as with whole numbers. (Divide, Multiply, Subtract, Check, Bring Down) 4. Place the decimal point in the quotient by moving it straight up from the dividend.
Divide. Show All Work!
1. 0.540
÷
0.6
2. 129
÷
0.3
3. 600.16
÷
0.62
4. 0.0092
÷
8
Simplifying Fractions and Ratios
A fraction is in simplest form when the greatest common factor (GCF) of the numerator and the denominator is 1.
Express 28:63 in simplest f orm
Factors of 28: 1 , 2, 4, 7, 14, 28 Factors of 63: 1 , 3, 7, 9, 21, 63 The GCF of 28 and 63 is 7.
To write in simplest form, divide the numerator and denominator by the GCF.
28
63
28
÷
7
4
9
=
=
or 4:963
÷
7
Express each fraction or ratio in simplest form.
1.
25
35
2. 36:80 3.54
66
4. 49:72Write two different fractions that can be expressed i n simplest form as each of t he following.
5.
3
5
6.1
7
Adding and Subtracting Fractions
To add and subtract fractions, rename the fractions w ith a common denominator as
necessary. Then add or subtract the numerators and simplify.
To find a common denominator, find the least common multiple of the d enominators by
listing or prime factorization.
Add or subtract. Write each sum or difference in simplest form.
1.
3
5
11
+
15
2.2
+
5
12
13
.5
+
3
7
4
4
–
1
5
8
8
4
–
11
9
3 4.8
+
2
15
9
5. 6.
Adding/Subtracting Mixed Numbers
To add or subtract mixed numbers:
• Add or subtract the fraction. Rename if necessary.
• Add or subtract the whole numbers.
• Simplify.
Add or subtract. Write each sum or difference in simplest form.
1.
3
4
+
1
3
2.12
27
3
1
8
−
5
4
8
3.9
5
−
5
3
12
4
4.7
3
12
+
5
10
4
5.5
3
–
3
8
4
6.1
2
2
+
1
2
9
Multiplying Fractions and Mixed Numbers
• To multiply fractions: Cross-simplify if possible. Multiply the numerators. Then
multiply the denominators. Simplify. You do not have to find a common
denominator.
• To multiply mixed numbers: Rename each mixed number as an improper fraction.
Multiply like fractions and simplify.
Multiply. Write each product in simplest form.
1.
13
×
7
2.21 13
4 35
×
5 14
3.28 3
×
17 4
4.2
3
2
×
1
5
7
5.12
×
3
8
6.5
4
1
×
2
9
7
Dividing Fractions and Mixed Numbers
To divide fractions and mixed numbers:
1. Write any mixed numbers as improper fractions.
2. Find the reciprocal of the divisor (Flip the second number over). 3. Cross-simplify.
4. Multiply numerator-by-numerator and denominator-by-denominator. 5. Simplify.
Divide. Write in simplest form.
1.
7 1
÷
8 4
2.2 5
÷
5 8
3.8
÷
1
4
4.1
24
÷
1
2
5.1
2
÷
1
13
7
14
6.1
5
7
÷
2
2
6
Evaluating Expressions
An expression is a math statement that contains variables, numbers, and
operations. To evaluate an expression, first substitute the variables with numbers and then solve according to order of operations.
The order of o perations are: 1) Grouping (Parentheses). 2) Exponents. 3) Multiplication/Division (From Left to Right). 4) Addition/Subtraction (L to R)
Evaluate 11x – 7 if x = 8. 11(8) – 7. 88 – 7. 81
Evaluate each expression if r = 5, s = 2, x = 7, and u = 9.
1. 6 + 3u
3. 2
2. 4r – 10s
– 18
4. + 8
5.
6. 97 – (1/2s + x) + 5u
Graphing on the Coordinate Plane
• The coordinate plane is used to locate points.
• The coordinate plane is formed by the intersection of two n umber lines (x and y axis)
that meet at the origin (0,0).
• An ordered pair (x,y) is used to locate any point on the coordinate plane.
• The first number is called the x-coordinate, and the second number is called the
y-coordinate.
Graph each ordered pair on the coordinate plane to the right.
1. A(4,7) 2. B(-3, -2) 3. C(0, 5) 4. D(-4, 8) 5. E(-8,0) 6. F(0,0)
Refer to the coordinate plane to t he right. Write the ordered p air for each point.
7. A 8. B 9. C 10. D 11. E 12. F
I
<
I
•
I
•
•
>
-5 -4 -3 -2 -1 0 1 2 3 4 5<
I I
I
I
I
I
-5 -4 -3 -2 -1 0 !l 4I I I
I>
2 3 4 5 !l 4<
I I
I I
I
I
-5 -4 -3 -2 -1 0I I I I
2 3 4 5>
Comparing and Ordering Rational Numbers
Comparing Rational Numbers: When comparing rational numbers use the followinginequality symbols:
< is less than < is less than or
equal to > is greater than > is greater than or equal to
Example: 10 > 8 (10 is greater than 8)
Compare the following using an inequality symbol.
1. -5 ____ -9 2. 16 l ___ 16.5
4
II
Plotting points on a number line: Draw a number line and then put a point at the
location of that number.
Example: -4, 5, 1.5, -2, 0
Plot the following on the number line given.
3. {3, -1, 4.5, -3} 4. {-5, 2, -3.5, 4}
Ordering Rational Numbers: To order, convert all numbers to decimals. Then line up the
numbers on the decimal point, use trailing zeros to fill out each number to the same number of decimal digits, and then compare.
Example: {-1.5, 4, -3, }
-3 < -1.5 < , < 4
Put the following rational numbers in order from least to greatest.
2D Geometry
To find the area of a 2 dimensional figure, you must know the formulas. A few things to remember:
1. The base and height are perpendicular (they form a right angle). 2. In a trapezoid, the two bases are parallel (they do not intersect). 3. Base is any flat side. Use the one that has the height drawn to it.
4. For
π
use 3.14 or 227
Write the area formula for each shape.
1. Rectangle 2. Parallelogram
3. Triangle 4. Trapezoid
Find the area of each figure.
5.
6. 5cm 8cm12.6 cm 6.4 cm
15 cm
7.
L
6cm
8. 12 In. 9. I I I I I lOm1 I Ii]
_ - -
L - - - ~ 14m 10.Gem
11. 10 5 10 11 12.2.5cv
Adding Integers
Adding Integers with the Same Signs: Add the number together and
keep the sign.
-7 + -6 = -13
Adding Integers with Different Signs: Subtract the numbers and use the
sign of the number with the greater absolute value.
-7 + 6 = -1
7 + (-6) = 1
Find each sum. No Calculator.
1. 5 + (-8) 2. -6 + 6 3. -4 + (-9)
4. -7 + 13 5. -9 + (-9) 6. 14 + (-27)
7. 15 + (-10) 8. 19 + (-10) 9. -12 + (-18)
10. -14 + (-12) 11. -12 + (-8) 12. -28 + 16
Subtracting Integers
Change each subtraction problem into an addition problem, by
adding the opposite number, and then use the rules for adding
integers.
-10 – 15
-10 – (-15)
-10
+
(
-
15) = -25
-10
+
(
+
15) = 5
Rewrite each subtraction problem as an addition problem and then
find each sum. No Calculator.
1. 6 – (-8) 2. -2 - 3 3. -8 – (-10)
4. 9 – 14 5. 36 – (-12) 6. 5 – 12
7. 15 – (-8) 8. -16 – 6 9. -4 – 9
10. -17 – 13 11. -12 – (-9) 12. 14 – (-22)
Multiplying Integers
Multiply the numbers together and use the following rules…
negative
negative = positive
negative
positive = negative
Remember multiplication is commutative, so order doesn’t matter.
-7(-6) = 42
7(-6) = -42
Find each product. No Calculator.
1. 2(-8) 2. -3(-4) 3. 8(-4)
4. (-5)(-5) 5. -12(5) 6. -12(13)
7. 14(-3) 8. -14(-5) 9. -7(-8)
10. (-4)2 11. (-11)2 12. (-5)3
Dividing Integers
Divide the numbers together and use the following rules…
negative
÷
negative = positive
negative
÷
positive = negative
Once again in deciding whether the answer is negative or positive, order
doesn’t matter.
42
÷
(-6) = -7
-42
÷
(-6) = 7
Find each quotient. No Calculator.
1. -16 ÷ (-4) 2. -100 ÷ 10 3. -28 ÷ 7
4. 52 ÷ (-4) 5. -125 ÷ (-25) 6. -32 ÷ (-16)
7. -120 ÷ (-12) 8. 45 ÷ (-9) 9. 33 ÷(-3)
10. -36 ÷12 11. -200 ÷ (-25) 12. -88 ÷11
