ASVAB Arithmetic Reasoning Practice Test 572659

Questions 5
Topics Integers, Multiplying & Dividing Fractions, Percentages, Simplifying Radicals, Square Root of a Fraction

Study Guide

Integers

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

Multiplying & Dividing Fractions

To multiply fractions, multiply the numerators together and then multiply the denominators together. To divide fractions, invert the second fraction (get the reciprocal) and multiply it by the first.

Percentages

Percentages are ratios of an amount compared to 100. The percent change of an old to new value is equal to 100% x \({ new - old \over old }\).

Simplifying Radicals

The radicand of a simplified radical has no perfect square factors. A perfect square is the product of a number multiplied by itself (squared). To simplify a radical, factor out the perfect squares by recognizing that \(\sqrt{a^2} = a\). For example, \(\sqrt{64} = \sqrt{16 \times 4} = \sqrt{4^2 \times 2^2} = 4 \times 2 = 8\).

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, \(\sqrt{9 \over 16}\) = \({\sqrt{9}} \over {\sqrt{16}}\) = \({3 \over 4}\)