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Math 8/7

Lesson 67

Geometric Solids

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Dimensions

Geometric solids are shapes that take up space.

Geometric solids are three-dimensional.

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Polyhedra

Polyhedra have faces, edges, and vertices

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0011 0010 1010 1101 0001 0100 1011Prisms

Prisms are polyhedra with congruent opposite faces

A rectangular prism consists of opposite congruent rectangles

A triangular prism has a pair of opposite congruent triangles

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0011 0010 1010 1101 0001 0100 1011Non-Polyhedra

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0011 0010 1010 1101 0001 0100 1011Properties of Geometric Solids

All Geometric Solids have properties:

Surface Area the sum of the area of each face

Volume how much liquid the solid would hold

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0011 0010 1010 1101 0001 0100 1011Practice Problems

1. Acube has how many (a) faces , (b) edges , and (c) vertices?

2. Atriangular prism has how many a) faces , (b) edges , and (c) vertices?

3. If each edge of a cube is 3 cm, what is the surface area?

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Math 8/7

Lesson 68

Algebraic Addition

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0011 0010 1010 1101 0001 0100 1011What is Algebraic Addition

Algebraic addition is the addition ofpositive and negative integers.

In order to understand algebraic addition,

you need to understand opposites

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0011 0010 1010 1101 0001 0100 1011What are Opposites?

To get the opposite of a number, change the sign

Opposites are equidistant from 0 on the number line

Opposites have the same absolute value, but have different signs

The sum of opposites equal 0

When two numbers are opposites, they are a pair of opposites

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The negative sign (-)

-n is equal to the opposite ofn

A negative sign changes the sign ofn

If n = 2, then

n = -2. -2 is the opposite of 2.

If n = -13,then n = -(-13) = 13. 13 is the opposite of -13.

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0011 0010 1010 1101 0001 0100 1011How to Add Algebraically

Simplify 7 + (-3)

To add positive and negative integers, subtract the smaller number from

the larger number.T

he sum will have the sign of the larger number. So7+(-3) = 4

Simplify -3 (-2)

1. Turn this into an addition problem = > (-3) + [-(-2)]

2. [-(-2)] means the opposite of-2 So [-(-2)] = 2

3. So we have (-3) + [-(-2)] = (-3) + 2 = -1

Simplify -(-2) - 5 - (+6)

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0011 0010 1010 1101 0001 0100 1011Practice Problems

Use algebraic addition to find the following sums:

a. (-3) (+2)

b. (-3) (-2)

c. (+3) (2)

d. (-3) (+2) (-4)

e. (-8) + (-3) (+2)

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Math 8/7

Lesson 69

More on Scientific Notation

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Review Lesson 51

Scientific Notation for Large NumbersScientific notation is a way of expressing very large or very

small numbers as a product of a decimal number and a

power of 10.

For example, 9,461,000,000,000 can be expressed as

9.461 * 1012

In scientific notation, the power of 10 indicates where the

decimal point is located when the number is written instandard form.

a. Write 40,720,000 in scientific notation

b. Write 2.46 * 108 in standard form.

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Two-Step Scientific Notation

When the number in scientific notation is not in decimal form,

we must use a two-step process to write it in scientific

notation.

For example, the number 4600 * 105 is not quite in scientific

notation.

1. Write 4600 in scientific notation => 4.6 * 103

2. Substitute the scientific notation in the original problem =>

4.6 * 103 * 105

3. Add the exponents => 4.6 * 108

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Practice Problems

Example 1: Write 25 * 10-5 in scientific notation

Example 2: Write 0.25 * 104 in scientific notation

Write each number in scientific notation:

a. 0.16 * 105

b. 24 * 10-7

c. 30 * 105

d. .75 * 10-8

e. 14.4 * 108

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Math 8/7

Lesson 70

Volume

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What is Volume?

Volume is the space occupied by a geometric solid.

Height, Width, and Length must all be in the same units (cm, inches, feet, yards, etc.)

Volume is expressed as units-cubed, i.e. cm3 , in.3 , ft.3 , yd.3 , etc

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Practice Problems

Example 1: What is the volume of a cube where each vertex is 1 cm long?

Example 2: What is the volume of a rectangular prism where the length is 3 cm,

the width is 5 cm, and the depth is 4 cm?

Example 3: What is the volume of a cube with these dimensions

4 inches deep, 4 inches wide, 4 inches, long?

Example 4: What is the volume of a rectangular prism with these dimensions -

6 feet deep, 10 inches wide, 4 inches long?