 42 lessons
 0 quizzes
 10 week duration

Measurements
An introduction to numerical computation. Emphasis is placed on scientific and engineering notation, the rule of significant figures, and converting between SI and Imperial units.

Fractions, Percentage, Ratios and Proportion
Emphasis here is placed on understanding fractions, percent, and using ratios to compare quantities and set up proportions to solve problems.

Introduction to Algebra

Factoring

Solving Equations

Functions and Graphs

Geometry
This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.
 Identify, measure, and calculate different types of straight lines and angles
 Calculate the interior angles of polygons
 Solve problems involving a variety of different types of triangles
 Calculate the area of a variety of different types of quadrilaterals
 Solve problems involving circles
 Calculate the areas and volumes of different solids
Combining Complex Fractions
When a fraction contains fractions in its numerator and/or its denominator, it’s called a complex fractions, otherwise it’s a simple fraction.
Examples of simple fractions:
$\frac{3}{5}or\frac{a}{b}\phantom{\rule{0ex}{0ex}}$Examples of complex fractions:
$\frac{{\displaystyle 2}}{{\displaystyle \frac{7}{9}}}or\frac{{\displaystyle \frac{8}{11}+5}}{{\displaystyle \frac{4}{5}}}or\frac{{\displaystyle \frac{5}{a}}}{{\displaystyle \frac{b}{c}}}\phantom{\rule{0ex}{0ex}}$To simplify a complex fraction, you have to ensure that you reduce individually the numerator and denominator into simple fractions. Once you’ve done that, then you can divide them out using the method that was taught in the previous lesson.
Question: Simplify. Leave your answers as improper fractions.
$\overline{)a}\frac{{\displaystyle \frac{2}{3}+\frac{3}{4}}}{{\displaystyle \frac{1}{5}}}\overline{)b}\frac{5\u2013{\displaystyle \frac{2}{5}}}{6+{\displaystyle \frac{1}{3}}}\phantom{\rule{0ex}{0ex}}$Answers:
(a) Start by combining the numerator fractions:
$\frac{2\left(4\right)+3\left(3\right)}{3\left(4\right)}=\frac{8+9}{12}=\frac{17}{12}\phantom{\rule{0ex}{0ex}}$Now the numerator and denominator are simple fractions:
$\frac{{\displaystyle \frac{17}{12}}}{{\displaystyle \frac{1}{5}}}=\frac{{\displaystyle 17}}{{\displaystyle 12}}\xf7\frac{{\displaystyle 1}}{{\displaystyle 5}}=\frac{{\displaystyle 17}}{{\displaystyle 12}}\times \frac{{\displaystyle 5}}{{\displaystyle 1}}=\frac{85}{12}\phantom{\rule{0ex}{0ex}}$Solution to (b)(b) We start by combining the numerator terms together, and the denominator terms too:
$\mathrm{Numerator}:5\u2013\frac{2}{5}=\frac{5\left(5\right)\u20132}{5}=\frac{23}{5}\phantom{\rule{0ex}{0ex}}\mathrm{Denominator}:6+\frac{1}{3}=\frac{6\left(3\right)+1}{3}=\frac{19}{3}\phantom{\rule{0ex}{0ex}}$Now the numerator and denominator are simple fractions:
$\frac{{\displaystyle \frac{23}{5}}}{{\displaystyle \frac{19}{3}}}=\frac{{\displaystyle 23}}{{\displaystyle 5}}\xf7\frac{{\displaystyle 19}}{{\displaystyle 3}}=\frac{{\displaystyle 23}}{{\displaystyle 5}}\times \frac{{\displaystyle 3}}{{\displaystyle 19}}=\frac{69}{95}\phantom{\rule{0ex}{0ex}}$
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The video below shows three examples of complex fractions being simplified. The first example is nonalgebraic, while the second and third are. Given how little we’ve focused on algebra thus far in this course, you may skip the last two questions, though the principles are the same.