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 Pre-algebra Arithmetics Integers Divisibility Decimals Fractions Exponents Percentages Proportional reasoning Radical expressions Graphs Algebra Monomials Polynomials Factoring Linear Equations Graphs of linear equations Rectangular Coordinate System Midpoint Formula Definition of Slope Positive and negative slope Determine the slope of a line Equations of lines Equation of lines (from graph) Applications of linear equations Inequalities Quadratic equations Graphs of quadratic equations Absolute Value Radical expressions Exponential equations Logarithmic equations System of equations Graphs and functions Plotting points and naming quadrants Interpreting Graphs Relations and Functions Function Notation Writing a Linear Equation from a Table Writing a Linear Equation to describe a Graph Direct Variation Indirect Variation Domain and range Sequences and series Matrices Inverse of a matrix Determinants Inner product Geometry Triangles Polygons 2-D Shapes 3-D Shapes Areas Volume Pythagorean Theorem Angles Building Blocks Geometry Transformations Parallel, coincident and intersepting lines Distances in the plane Lines in space Plane in space Angles in the space Distances in the space Similarity Precalculus Sequences and series Graphs Graphs Definition of slope Positive or negative slope Determine the slope of a line Equation of a line (slope-intercept form) Equation of a line (point slope form) Equation of a line from graph Domain and range Quadratic function Limits (approaches a constant) Limits (approaches infinity) Asymptotes Continuity and discontinuities Parallel, coincident and intersepting lines Introduction to Functions Limits Continuity Asymptotes Trigonometry Trigonometric ratios The reciprocal trigonometric ratios Trigonometric ratios of related angles Trigonometric identities Solving right angles Law of sines Law of cosines Domain of trigonometric functions Statistics Mean Median Mode Quartiles Deciles Percentiles Mean deviation Variance Standard Deviation Coefficient of variation Skewness kurtosis Frequency distribution Graphing statistics & Data Factorial Variations without repetition Variations with repetition Permutations without repetition Permutation with repetition Circular permutation Binomial coefficient Combinations without repetition Combinations with repetition

 Proportions Equal shares A number of people invest different amounts in a project. When it comes to sharing the profits of the project the usual method is that a person who initially invests more capital gets a larger share of the profits and whoever invests less capital receives a smaller share of the profits. That is, the division of profits is directly proportional to the amount of the initial investment. Direct equal shares Three business associates, Anthony, Joseph and Ana invest €5000, €8000 and €10000 respectively, to set up a company. After some time the company makes €2300 profit. What share of the profit does each investor receive? Let x, y and z represent the profits of Anthony, Joseph and Ana. Then we can work out the proportion of profit to  investment. So Antonio receives €500, José receives €800 and Ana receives 1000 euros. A charitable organization decides to donate 1390 computers to three schools in direct proportion to the number of their students. The first school has 230 students, the second one has 540 students and the third one, 620. How many computers will each school receive? The first school receives computers The second school receives computers The third school receives computers