# Page 3 Mathematical Reasoning Study Guide for the GED® test

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 at 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

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 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, 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 this 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 x 3 + 2 x 4
2 x 7 = 6 + 8
14 = 14

Exponents, cube 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 x 7 and $3^4$ = 3 x 3 x 3 x 3

The square root symbol (√) asks you to find the number that, when multiplied by itself, equals the given number. So, √4 = 2, because 2 x 2 = 4.

The cube root symbol is ∛. So, ∛125 = 5 because 5 x 5 x 5 = 125