  • Pre-Algebra
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 Arithmetics Signed numbers Divisibility Decimals Fractions Percentages Proporcional reasoning Mixture problems Prime numbers Factoring Prime factorization GCF LCM Radicals Exponential expressions Uniform Motion Problems Ratio Proportions Direct variation Inverse variation
 Monomials Polynomials Special products Linear equations Quadratic equations Radicals Simultaneous equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 Graphs Slope of a line Determine slope of line Equation of a line Equation of a line (from graph) Limits Quadratic function Parallel, coincident and intersecting lines Asymptotes Continuity and discontinuities Distances
 Law of sines Law of cosines
 Equations of a straight line Parallel, coincident and intersecting lines Distances Angles in space Inner product
 Factorial Variations without repetition Variations with repetition Permutations with repetition Permutations without repetition Exercises Circular permutations Binomial coefficient Combinations with repetition Combinations without repetition
 Arithmetic mean

 Proportions Ratio A ratio is a comparison of two numbers. Suppose we want to write the ratio of 8 and 12. We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve. The ratio of two numbers a and b is the quotient Sussan has a bag with 3 pens, 4 pencils, 7 felt tip pens, and 1 pencil sharpener. What is the ratio of pencils to pens? Expressed as a fraction, with the numerator equal to the first quantity and the denominator equal to the second, the answer would be 4/3. Two other ways of writing the ratio are 4 to 3, and 4:3. Proportion An equation in which two ratios are equal is called a proportion. Two ratios and are a proportion when Remember the two ratios are equals if their cross products are equal a·d = b·c You can also use the cross product to find a missing number: Find x to get a proportion . Find x to get a proportion Solution x=