## ASVAB Arithmetic Reasoning Practice Test 239230

 Questions 5 Topics Multiplying & Dividing Radicals, Negative Exponent, PEMDAS, Rates, Square Root of a Fraction

#### Study Guide

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

###### Negative Exponent

A negative exponent indicates the number of times that the base is divided by itself. To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal: $$b^{-e} = { 1 \over b^e }$$. For example, $$3^{-2} = {1 \over 3^2} = {1 \over 9}$$

###### PEMDAS

Arithmetic operations must be performed in the following specific order:

1. Parentheses
2. Exponents
3. Multiplication and Division (from L to R)
4. Addition and Subtraction (from L to R)

The acronym PEMDAS can help remind you of the order.

###### Rates

A rate is a ratio that compares two related quantities. Common rates are speed = $${distance \over time}$$, flow = $${amount \over time}$$, and defect = $${errors \over units}$$.

###### Square Root of a Fraction

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately. For example, $$\sqrt{9 \over 16}$$ = $${\sqrt{9}} \over {\sqrt{16}}$$ = $${3 \over 4}$$