Mathematical Reasoning Study Guide for the GED Test

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Operations

Addition, Subtraction, Multiplication, and Division of all types of numbers, fractions, decimals, roots, and exponents.

Undefined rational expressions: A rational expression is one that is written in the form of a fraction. The top number is the numerator and the bottom number is the denominator. If the denominator equals \(0\) (zero), the expression is undefined because you cannot divide by zero.

Multi-step problems with the four operations with rational numbers. These would be problems in which you have to perform two or more operations in order to find the answer. The key to these is knowing which operations to use and determining which numbers to use in each of them.

Scientific notation: This is simply a short way to write really long numbers. It uses a single digit whole number with decimal places and powers of 10 as a multiplier.

Example: The number \(4,3795\) can be written as \(4.3795 \times 10^4\) using scientific notation. The exponent for \(10\) tells how many places you moved the decimal point.

Calculation

Unit rates including determining unit pricing, constant speed, number of items in a certain area, like square yard, etc.

Example: Find the unit price of a grocery product by using how many ounces you get for a certain price. If you divide the price by the number of ounces, the answer would be the unit price.

Scale drawings: Often, drawings of large things are drawn “to scale” by using a small space to represent a larger one. Maps are a good example.

Example: To find the distance between two cities on a map, you would consult the map scale to find that \(\frac{1}{4}\) inch represents \(10\) miles. If there seems to be about an inch between the two cities on the map, the answer would be close to \(40\) miles.

Ratios and Proportions

A ratio is simply a way of comparing two quantities. If you have \(4\) dogs and \(2\) cats, the ratio of dogs to cats in your house is \(4\) to \(2\) and can be written \(4:2\) or \(\frac{4}{2}\).

A proportion is a way to show that two ratios are equal and can also be written using a colon or in fraction form.

If your friend has \(2\) dogs and \(1\) cat, you and your friend have the same ratios of dogs to cats. It is also correct to say that your ratio of dogs to cats is proportionate to your friend’s ratio of dogs to cats.

You may then write \(4:2 = 2:1\) or \(\frac{4}{2} = \frac{2}{1}\).

Percents

These include figuring out sale prices and tips, as well as percent of increase and decrease.

A percent (\(\%\)) is another way of saying, “per \(100\).” So, \(40\%\) means \(40\) of every \(100\).

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