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# Helpful Formulas for the Accuplacer Next Generation Arithmetic Test

The Accuplacer Next Generation Test has 3 math-related sections: Next Generation Arithmetic; Next Generation Quantitative Reasoning, Algebra, and Statistics; and Next Generation Advanced Algebra and Functions. The following chart gives you useful formulas that you’ll need to know if you want to ace the Arithmetic Section, but remember that it’s very unlikely that you’ll be able to use it during the test. However, we suggest you use this chart as a guide to know where your strengths and weaknesses are, and for a final review before the test.

Check our study guides for more detailed information, and try to use these formulas for solving the sample tests we have at Union Test Prep!

## Fractions

Formula Symbols Comment
$$\dfrac{a}{b}+\dfrac{c}{d} = \dfrac{(a \cdot d)+(c \cdot b)}{b \cdot d}$$ $$a, b, c, d = \text{ any real number}$$ Simplify the fraction (if possible).
$$\dfrac{a}{b} \cdot \dfrac{c}{d} = \dfrac{a \cdot c}{b \cdot d}$$ $$a, b, c, d =\text{ any real number}$$ Simplify the fraction (if possible).
$$\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a \cdot d}{b \cdot c}$$ $$a, b, c, d =\text{ any real number}$$ Simplify the fraction (if possible).
$$a \frac{b}{c} = \dfrac{(a\cdot c)+b}{c}$$ $$a, b, c=\text{ any real number}$$ Simplify the fraction (if possible).

## Percents

Formula Symbols Comment
$$a \cdot b\% = a \cdot \dfrac{b}{100}$$ $$a = \text{ any real number}$$
$$b \%= \text{ any percent}$$
Simplify (if possible).
$$\%=\dfrac{\lvert b-a \rvert}{b} \cdot 100 = \dfrac{c}{b} \cdot 100$$ $$\% = \% \text{ increase or decrease}$$
$$a= \text{ new value}$$
$$b= \text{ original value}$$
$$c= \text{ amount of change}$$