PRE-ALGEBRA 7TH

Rational numbers:A rational number is a point on the number line that can be written (represented, expressed) as a ratio (fraction) of a whole number and a natural number , where cannot be 0.

PERCENTS

GEOMETRY

STATISTICS AND PROBABILITY

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EXPRESSIONS, EQUATIONS AND INEQUALITIES

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EQUATION:An equation is a mathematical sentence that has two equal sides separated by an equal sign. 4 + 6 = 10 is an example of an equation. We can see on the left side of the equal sign, 4 + 6, and on the right hand side of the equal sign, 10. Example: 3x – 5 = 16 x= 7

Expression:An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)Example: 2x + 3

RATIOS AND PROPORTIONS

INEQUALITITES:An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b.Example:
x + 3 > 2 x=-1

4 GEOMETRY FACTS

Geometry skills

Adjacent angles:Two angles that have a common side and a common vertex (corner point), and don't overlap.

Angles on a point: The measure of all angles formed by three or more rays with the same vertex is 360 degrees

Vertical angles: Two angles are vertical angles(or vertically opposite angles) if their sides form two pairs of opposite rays

Angles on a line: The sum of the measures of two angles that share a ray and form a line in 180 degrees

Area:The area of a figure is the number of unit squares that cover the surface of a closed figure. The area is measured in square units such as square centimeters, square feet, square inches, etc.

Surface area is the amount of space covering the outside of a three-dimensional shape.

Perimeter is the total length of the sides of a two-dimensional shape. We often find the perimeter when putting up Christmas lights around the house or fencing the backyard garden.

Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Statistics: A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data.


For example, the parameter may be the average height of 25-year-old men in North America. The height of the members of a sample of 100 such men are measured; the average of those 100 numbers is a statistic.

Probability tells you the likelihood of an event happening. The lower the probability, the less likely it is to happen. The higher the probability, the more likely it is to happen. Probability is a number or fraction between 0 and 1.

For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

Tax:Money that the government collects based on income, sales, and other activities.

Tax amount = Final price - Price before tax = $25 - $20 = $5.

Tip: A tip is typically a percentage of a total cost, and they are given in appreciation of a service.

Commission: fee paid for services, usually a percentage of the total cost.

Using the same example, calculating a 15% tip on a $45 bill would be: $45 * 0.15 = $6.75.

Example: City Gallery sold Amanda's painting for $500, Amanda paid them a 10% commission (of $50), and so ended up with $450 for the painting.

Mark-up: The amount which you increase the price to cover the cost is known as markup. For example, if you buy a video game for $20, you must sell it at more than $20 to make a profit. The amount you increase the price by can be expressed as a percent of the purchase price.

Example: You buy a game for 20$ and sell it for 30$

Mark-down:A markdown is an amount by which you decrease the selling price. The amount that you decrease the price by can be expressed as a percent of the selling price, known as the markdown rate. The selling price would be determined using the equation

Example: Sell a game for 40$ but have a discount/markdown for a sale of 20% and sell it for 32$

Absolute value:Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative

Integers:Integers. Integers are whole numbers, including negative and positive numbers and zero; they don't contain fractions or decimal parts

Fraction: A fraction shows part of a whole

Example:The absolute value of 5 is 5, and the absolute value of −5 is also 5

Adding: 4+(-5) = -1

Subtracting: -2 + 5 = 3

Multiplying:–2 × –3 = 6

Dividing:-6 ÷ 2= -3

Adding= 1/2 + 2/4 = 1

Subtracting= 4/6 - 1/3 = 2/6

Multiplying= 1/4 × 5/8 = 5/32

Dividing= 8/5 ÷ 5 = 8/5 × 1/5 = 8/25