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

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It’s great that you’re preparing to take the ParaPro Test so you can teach math in the future. And we want to help you reach that goal because our vision is a world full of people like you!

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
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