Pre-Algebra Formulas

  • $X$% of $Y$ $$X\%\;\mbox{of}\;Y=\Big(\frac{X}{100}\Big)\times Y$$
  • $X$ is What % of $Y$ $$\mbox{What %}=\Big(\frac{X}{Y}\Big)\times 100$$
  • Percentage Change $$\mbox{% change}=\frac{\mbox{Final Value}-\mbox{Initial Value}}{\mbox{Initial Value}}\times 100$$
  • Percentage Increase $$\mbox{Percent increase}=\frac{\mbox{To Value} - \mbox{From Value}}{\mbox{From Value}}\times 100$$
  • Percentage Decrease $$\mbox{Percent decrease}=\frac{\mbox{From Value} - \mbox{To Value}}{\mbox{From Value}}\times100$$
  • Fraction Formulas
    • Fractions Addition $$\frac ab+\frac cb=\frac{a+c}b,\;\mbox{for} \;b\ne0$$ $$\frac ab+\frac cd=\frac{a\times d+c\times b}{b\times d},\;\mbox{for} \;b,d\ne0$$
    • Fraction Subtraction $$\frac ab-\frac cb=\frac{a-c}b,\;\mbox{for} \;b\ne0$$ $$\frac ab-\frac cd=\frac{a\times d-c\times b}{b\times d},\;\mbox{for} \;b,d\ne0$$
    • Fractions Multiplication $$\frac ab\times\frac cd=\frac{a\times c}{b\times d},\;\mbox{for} \;b,d\ne0$$
    • Fraction Division $$\frac ab\div\frac cd=\frac ab\times\frac dc=\frac{a\times d}{b\times c},\;\mbox{for} \;b,c,d\ne0$$
  • Ratio & Proportion - 2 Numbers $$\mbox{Simplified Ratio}=\frac{a}{GCF(a,b)}\div \frac{b}{GCF(a,b)}$$
  • Arithmetic Progression $$\mbox{$n^{th}$ term}\; a_n =a_1+(n-1)d$$ $$\mbox{Sum}\;S_n=\frac{n}{2} \big[2a_1+(n-1)d\big]$$
  • Geometric Progression $$\mbox{$n^{th}$ term}\; g_n =g_1r^{n-1},\;\mbox{for}\;n\geq2$$ $$\mbox{Sum}\;S_n=\left\{ \begin{array}{ll} \frac{g_1(1-r^n)}{1-r}, & r\ne1; \\ n g_1, & r=1 \end{array} \right.$$
  • Sum of Squares & Cubes of first $n$ natural numbers $$\mbox{Sum of Squares}=1^2+2^2+\ldots+n^2=\sum_{i=1}^n i^2=\frac{n(n+1)(2n+1)}{6}$$ $$\mbox{Sum of Cubes}=1^3+2^3+\ldots+n^3=\sum_{i=1}^n i^3=\Big(\frac{n(n+1)}{2}\Big)^2$$
  • Sum and Difference of Cubes $$a^3+b^3=(a+b)(a^2-ab+b^2)$$ $$a^3-b^3=(a-b)(a^2+ab+b^2)$$
  • Pythagorean Theorem
    $Right$ $triangle$ $c^2 = a^2 + b^2$
    $b^2 = c^2 - a^2$
    $a^2 = c^2 - b^2$
    Pythagoras Theorem Formula

Pre-Algebra Formulas Reference

Pre-algebra formulas reference is the collection equations for the study of basic mathematics. This formulas cheatsheet includes numbers, integers, fractions, decimals, negative numbers, factorization, roots, powers, radical numbers, associativity, distributivity and more. It is a complete list of pre-algebra formulas to prepare student for the study of algebra.