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Using Percents

*Percent means ”out of 100″.

*A percent is a special way of representing a fraction with a denominator of 100.

* 5 percent means 5 cents for every dollar.

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5 percent = 5% or .05 or 5/100

65 percent = 65% or .65 or 65/100

125 percent = 125% or 1.25 or 125/100

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discount: an amount of money subtracted from a regular price

tax: an amount of money added onto products or services by the government

tip: a gift of money added onto a food bill, for good service

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Changing a Fraction to a Percent

1/4 = 1 ÷ 4 = .25 = 25% OR:

1/4 = 25/100 = 25% (Multiply denominator by the number that will give you 100. Then multiply numerator by same number.)

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Equivalent Fractions

Create equivalent fractions by multiplying or dividing the numerator and denominator by the same number.

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Changing Improper Fractions to Mixed Numbers:

Divide the numerator by the denominator. Write the remainder as a fraction.

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Greatest Common Factor

To find the greatest common factor of two numbers:

8 and 12

1. Write all factors of the numbers from smallest to largest.

8 : 1, 2, 4, 8

12: 1, 2, 3, 4, 8, 12

2. Write, or circle, all the factors the two numbers have in common: 1, 2, 4, 8

3. The greatest (largest) common factor is: 8.

 

 

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Adding “Like” Fractions (fractions with the same denominator)

1. Add the numerators. Write the answer as the numerator in the new fraction.

2. Bring down the denominator.

3. Write the answer in simplest form by dividing the numerator and denominator by their greatest common factor.

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Adding “Unlike” Fractions (fractions with different denominators)

1. Rewrite the fractions as equivalent fractions with the least common denominator.

2. Add the numerators.

3. Bring down the denominator.

4. Write the answer in lowest terms (simplest form).

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Finding the Least Common Denominator

1. List the multiples for each denominator, beginning with the lowest multiple.

2. Continue until you find the lowest number that is ‘common’ to both denominators.

Example: Finding the least common denominator of 1/4 and 5/6:

Multiples of 4 = 4, 8, 12, …

Multiples of 6 = 6, 12, …

12 is the least common denominator (or LCD).

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  Use the Factor Tree

1. Factor each number to its prime numbers

2. Identify common prime numbers

3. Identify prime numbers that are left.

3. Multiply common prime number and the leftover prime numbers.

Example:

 4 = 2, 2

 6 = 2, 3

Common prime number is 2

 Leftover prime numbers are 2 and 3

LCM/LCD = 2 x 3 = 6 

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Variables and Patterns

A coordinate graph is a way to show the relationship between two variables.

variable- a quantity that can change

The dependent variable depends on the independent variable and goes on the y axis.

The time variable usually goes on the x axis.

scale- a plan for how to space the numbers on the axes on a coordinate grid.

interval- the space between each numbered value on a coordinate graph or in a table of values.

x axis- the number line that is horizontal on a coordinate grid

y axis- the number line that is vertical on a coordinate grid

coordinate pair- an ordered pair of numbers used to locate a point on a coordinate grid. (The first number is the value for the x coordinate.) (x,y)

*We connect points on a coordinate graph when it makes sense to consider what is happening in the intervals between the points.

equation or formula- a rule containing variables that represents a mathematical relationship

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Integers

Positive Numbers: Numbers greater than 0

Negative Numbers: Numbers less than 0

Zero is neither positive nor negative.

Opposites are numbers that are the same distance from 0, but on different sides of 0.

The whole numbers are: 0, 1, 2, 3, 4, …

Integers include positive and negative whole numbers and 0.

Examples of a number sentence: 3 + 4 = 7

4 — 9 = ¯ 5

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Absolute Value: The distance a number is from zero.

l -2 l = 2 l 2 l = 2

Rules for Calculating with Integers:

Addition:

1. The sum of two negative integers is a negative integer.

¯ 6 + ¯ 4 = ¯ 10.

2. The sum of a negative integer and a positive integer is sometimes a negative integer and sometimes a positive integer.

¯ 7 + 1 = ¯ 6

¯ 5 + 8 = 3

*If the negative integer is larger: (7 > 1), the sum (answer) will be negative.

* If the positive integer is larger: (8 > 5), the sum (answer) will be positive.

**(If the absolute value of the positive integer is larger than the absolute value of the negative integer, the answer will be a positive integer.)

Subtraction:

1. When you subtract two negative integers, you sometimes get a negative number and sometimes a positive: ¯ 5 — ¯ 3 = ¯ 2

¯ 4 — ¯ 7 = 3

2. When you subtract a positive and a negative integer, you sometimes get a negative integer and sometimes a positive:

¯ 6 — 4 = ¯ 10

7 — ¯3 = 10

*If you subtract a smaller integer from a greater integer, you get a positive result.

*If you subtract a greater integer from a smaller integer, you get a negative result.

Multiplication: Multiplying a positive and a negative integer always gives a negative result. 2 x ¯7 = ¯ 14

Division: Division is the opposite of multiplication. You can write a division sentence that undoes the multiplication.

35 ÷ ¯ 7 = ¯5

¯12 ÷ 4 = ¯ 3

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Probability

Probability: the chance that a particular outcome will occur, or:

: a number between 0 and 1 that describes the likelihood that an event will occur

: a probability is expressed as a ratio of favorable outcomes compared to the total possible outcomes

Theoretical Probability: an expected probability; (written as a fraction):

number of favorable outcomes/number of possible outcomes

Experimental Probability: a probability that is determined through experimentation;

number of trials that result in a planned outcome/number of total trials

 

Surface Area

Surface Area: the total of the areas of all the surfaces of a solid.

Surface Area of a rectangular prism: the sum of the areas of each of its six faces.