# Mathematics I (Math 1132)

Durham College, Mathematics
Free
• 0 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.

• ##### Geometry

This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.

## Mathematics I (Math 1132)

### 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:

Examples of complex fractions:

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.

(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:

$\frac{\frac{17}{12}}{\frac{1}{5}}=\frac{17}{12}÷\frac{1}{5}=\frac{17}{12}×\frac{5}{1}=\frac{85}{12}\phantom{\rule{0ex}{0ex}}$
Solution to (b)

(b) We start by combining the numerator terms together, and the denominator terms too:

Now the numerator and denominator are simple fractions:

$\frac{\frac{23}{5}}{\frac{19}{3}}=\frac{23}{5}÷\frac{19}{3}=\frac{23}{5}×\frac{3}{19}=\frac{69}{95}\phantom{\rule{0ex}{0ex}}$

[collapse]

The video below shows three examples of complex fractions being simplified. The first example is non-algebraic, 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.