Mathematical Reasoning Study Guide for the GED Test

Question Types:

Fill-in-the-blank

You will type a short response in the box provided, using 10 minutes or less.

Drag-and-drop

Here, you will click and drag an item from one place on the screen to another. You might be asked to do this in order to show in which category an item belongs or to show when it occurred on a timeline.

Drop-down

You will be asked to pick an answer from a pull-down menu on the screen. After you select your answer, it will become part of the text on the screen so that you can see how it fits.

Hot spot

When answering this type of question, you will be asked to click on the spot on the screen that shows the correct place or answer. This type of question may be used to allow you to indicate points on a graph or to mark parts of a geometric figure.

Question Subject Matter

The questions on the Math Reasoning section of the GED test come from two major areas of math. About 45% of the questions deal with quantitative problem-solving and the other 55% concern problem-solving in Algebra. The questions are on a level that would be necessary for people entering college or the workforce. There is a focus on applying math to real-life situations, from both academic and workforce environments.

Here are some concepts you will want to review as you practice. Very basic and brief explanations are offered here, but you also need to be able to use all of them in problem-solving and know the rules for doing so. If you run into something that you don’t fully understand or know how to use in math, there are many online drill and practice sites. Just search for the term and you should be able to find them.

Quantitative Concepts: Numeration

Rational number

A rational number is any number that can be written as a simple fraction, including all integers.

These are rational:

the fraction \(\frac{1}{3}\)
\(5\) (can be written as \(\frac{5}{1}\))
\(0.25\) (can be written as \(\frac{1}{4}\))
\(0.33…\) (because it repeats forever and can be written as \(\frac{1}{3}\))

What is an irrational number? Basically, any number whose decimal never repeats, such as Pi \((3.14…)\).

Absolute value

The absolute value just tells how far a number is from zero and is written using two vertical lines around the number.

\(\vert5\vert = 5\) (Read: The absolute value of \(5\) is \(5\).)
\(\vert-5\vert = 5\). It is also \(5\) places from \(0\), just in the opposite direction.

Fractions

Be sure that you know how to do the four operations (add, subtract, multiply, and divide) with fractions and how to simplify fractions.

Simplifying fractions examples:

\[\frac{4}{8} = \frac{1}{2}\] \[\frac{22}{11} = 2\] \[\frac{8}{3} = 2\frac{2}{3}\]

Decimals

Practice doing the 4 operations with decimal numbers and being sure the decimal point is in the right place in the answer. Also, be sure you can identify the largest or smallest number in a group of numbers with decimal places.

Example:

Of these numbers, which has the greatest value?

\(0.137\)
\(0.0137\)
\(0.00137\)
\(0.1037\)

The answer is \(0.137\)

Factors

Be familiar with factors, including the greatest common factor of two numbers. A factor of a number can be multiplied by another number to equal the first number.

Example: \(4\) and \(3\) are both factors of \(12\)

The greatest common factor of \(2\) numbers is the largest number that is a factor of both of the two numbers.

Factors of \(12: \; 2, \;3, \;4, \;6\)
Factors of \(18: \; 2, \;3, \;6, \;9\)

\(2, \;3,\) and \(6\) are all common factors and \(6\) is the greatest common factor of \(12\) and \(18\)

Multiples

Be familiar with multiples, including the least common multiple of two numbers. A multiple is a number that can be reached by multiplying the given number by another number. A common multiple is a number that is a multiple of 2 numbers.

\(5, \;10, \;15, \;20, \;25, \;30, \;35, \;40, \;45\) are multiples of \(5\) \(4, \;8, \;12, \;16, \;20, \;24,\; 28, \;32,\; 40\) are multiples of \(4\)

\(20\) and \(40\) are common multiples of \(5\) and \(4\)
\(20\) is the least common multiple of \(5\) and \(4\)

Number lines

Be familiar with number lines, especially being able to accurately place a point on a number line if each point on it is not numbered.

Distributive property

You should be able to use the distributive property property with real numbers as well as in algebraic expressions and equations.

This property states that:

\[a(b + c) = ab + ac\]

So,

\(2(3 + 4) = 2 \times 3 + 2 \times 4\)
\(2 \times 7 = 6 + 8\)
\(14 = 14\)

Exponents, cube roots, and square roots of positive, rational numbers.

An exponent is a small number written to the right and slightly above another number. It tells how many times to multiply the number by itself.

\(7^2 = 7 \times 7\) and \(3^4\) = \(3 \times 3 \times 3 \times 3\)

The square root symbol (\(\sqrt{}\)): asks you to find the number that, when multiplied by itself, equals the given number. So, \(\sqrt{4} = 2\), because \(2 \times 2 = 4\).

The cube root symbol is \(\sqrt[3]{}\). So, \(\sqrt[3]{125} = 5\) because \(5 \times 5 \times 5 = 125\)