## ASVAB Arithmetic Reasoning Practice Test 732855

 Questions 5 Topics Absolute Value, Commutative Property, Distributive Property - Division, Multiplying & Dividing Radicals, Rational Numbers

#### Study Guide

###### Absolute Value

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: $$\left|-5\right| = 5$$. In the case of a variable absolute value ($$\left|a\right| = 5$$) the value of a can be either positive or negative (a = -5 or a = 5).

###### Commutative Property

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

###### Distributive Property - Division

The distributive property for division helps in solving expressions like $${b + c \over a}$$. It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: $${b + c \over a} = {b \over a} + {c \over a}$$. For example, $${a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6$$.

###### Multiplying & Dividing Radicals

To multiply or divide radicals, multiply or divide the coefficients and radicands separately: $$x\sqrt{a} \times y\sqrt{b} = xy\sqrt{ab}$$ and $${x\sqrt{a} \over y\sqrt{b}} = {x \over y}\sqrt{a \over b}$$

###### Rational Numbers

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form $${a \over b}$$ where a is the numerator and b is the denominator. An improper fraction ($${5 \over 3}$$) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number ($$1 {2 \over 3}$$) which has a whole number part and a fractional part.