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Formulas for the Arithmetic Questions on the GRE® Quantitative Reasoning Test

If you’re preparing for the GRE® Test, and you want to get the best score possible in the Quantitative Reasoning section, you have come to the right place! At Union Test Prep, we believe in you and want you to succeed. Below, we have the essential formulas you’ll need to use for the arithmetic questions found on the GRE® Quantitative Reasoning Test. Check out our GRE® blogs for formula charts that relate to the other types of Quantitative Reasoning problems on the GRE®.

And if you are a bit rusty with math, it doesn’t matter—you can also check our other resources:

complete study guide for GRE® Quantitative Reasoning Test

practice questions GRE® Quantitative Reasoning Test

flashcards GRE® Quantitative Reasoning Test

Remember that this chart only shows formulas for one part of the test: Arithmetic. Access our other three formula charts for the GRE® Quantitative Reasoning section, here:

Algebra

Geometry

Data Analysis

Formula Symbols Comment
\(\dfrac{a}{b} + \dfrac{c}{d}= \dfrac{(a\cdot d) + (c \cdot b)}{b\cdot d}\) a, b, c, d = any real number simplify (if possible)
\(\dfrac{a}{b} \cdot \dfrac{c}{d} = \dfrac{a\cdot c}{b\cdot d}\) a, b, c, d = any real number simplify (if possible)
\(\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a \cdot d}{b \cdot c}\) a, b, c, d = any real number simplify (if possible)
\(a \frac{b}{c} = \dfrac{(a\cdot c) + b}{c}\) a, b, c = any real number simplify (if possible)
\(a \cdot b \% = a \cdot \frac{b}{100}\) a = any real number
b% = any percent
simplify (if possible)
\(\% = \dfrac{\vert{b-a}\vert}{b} \cdot 100 = \dfrac{c}{b} \cdot 100\) % = % increase or decrease
a = new value
b = original value
c = amount of change
 
\(x^a \cdot x^b = x^{a+b}\) a, b, x = any real number  
\(\dfrac{x^a}{x^b} = x^{a-b}\) a, b, x = any real number \(x \ne 0\)
\((x^a)^b = x^{a\cdot b}\) a, b, x = any real number  
\((x \cdot y )^a = x^a \cdot y^a\) a, x, y = any real number  
\(x^1 = x\) x = any real number  
\(x^0= 1\) x = any real number \(x \ne 0\)
\(x^{-a} = \dfrac{1}{x^a}\) a, x = any real number \(x \ne 0\)

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