Formulas for Math on the ParaPro Test: Part 1—Number Sense and Algebra

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Here you’ll find the essential formulas you’ll need for the math questions that deal with Number Sense and Algebra on the ParaPro Test. Other questions on the ParaPro Test require additional formulas, so check out our charts for those:

Formulas for ParaPro Geometry and Measurement Questions

Formulas for ParaPro Data Analysis Questions

Use the three charts to solve these: free ParaPro math practice questions at Union Test Prep

Number Sense and Algebra Formulas for the ParaPro Test

Category	Formula	Symbols	Comment
Number Sense and Algebra	\(a + b = b+ a\) \(a \cdot b = b\cdot a\)	\(a, b =\) any constant or variable	Commutative Property
Number Sense and Algebra	\(a + (b + c) = (a+b)+c\) \(a\cdot(b\cdot c) = (a\cdot b) \cdot c\)	\(a,b, c =\) any constant or variable	Associative Property
Number Sense and Algebra	\(a\cdot(b+c) = a\cdot b + a\cdot c\)	\(a,b,c =\) any constant or variable	Distributive Property
Number Sense and Algebra	\(a+0 = a\)	\(a =\) any constant or variable	Identity Property of Addition
Number Sense and Algebra	\(a\cdot 1 = a\)	\(a =\) any constant or variable	Identity Property of Multiplication
Number Sense and Algebra	\(\frac{a}{b} + \frac{c}{d} = \dfrac{a\cdot d + c\cdot b}{b\cdot d}\)	\(a,b, c, d =\) any constant or variable	Remember to simplify the fraction (if possible)
Number Sense and Algebra	\(\frac{a}{b} \cdot \frac{c}{d} = \frac{a\cdot c}{b \cdot d}\)	\(a,b,c,d =\) any constant or variable	Remember to simplify the fraction (if possible)
Number Sense and Algebra	\(\frac{a}{b} \div \frac{c}{d} = \frac{a\cdot d}{b \cdot c}\)	\(a,b,c,d =\) any constant or variable	Remember to simplify the fraction (if possible)
Number Sense and Algebra	\(a \frac{b}{c} = \frac{a\cdot c + b}{c}\)	\(a,b,c =\) any constant or variable	Remember to simplify the fraction (if possible)
Number Sense and Algebra	\(a\cdot b\% = a \cdot \frac{b}{100}\)	\(a =\) any real number \(b \% =\) any percent	Remember to simplify the fraction (if possible)
Number Sense and Algebra	\(x^a \cdot x^b = x ^{a+b}\)	\(a,b,x =\) any real number
Number Sense and Algebra	\(\dfrac{x^a}{x^b} = x^{a-b}\)	\(a,b,x =\) any real number
Number Sense and Algebra	\((x^a)^b = x^{a \cdot b}\)	\(a,b,x =\) any real number
Number Sense and Algebra	\((x\cdot y )^a = x^a \cdot y^a\)	\(a,b,x,y =\) any real number
Number Sense and Algebra	\(x^1 = x\)	\(x =\) any real number
Number Sense and Algebra	\(x^0 = 1\)	\(x =\) any real number (\(x \ne 0\))
Number Sense and Algebra	\(x^{-a} = \dfrac{1}{x^a}\)	\(a,x =\) any real number (\(x \ne 0\))
Number Sense and Algebra	\(x+a = b \rightarrow x = b-a\) \(x-a = b \rightarrow x = b+a\) \(x\cdot a = b \rightarrow x= b \div a\) \(x\div a = b \rightarrow x = b \cdot a\) \(x^a = b \rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x} = b \rightarrow x = b^a\) \(a^x = b \rightarrow x = \dfrac{ log \; b}{log \; a}\)	\(a,b =\) constants \(x =\) variable