Mathematics I (Math 1132) Durham College, Mathematics
Free • 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.

• Geometry

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

Mathematics I (Math 1132)

Solve Proportion Equations

You were introduced to ratios and proportions a few units ago, but you hadn’t acquired the skills to solve equations. Now that you know the techniques to solving equations, you can finally begin to solve proportion-related equations and word problems.

The simplest type of proportion equation to solve is when you have one ratio equal to another, as shown below:

To solve this, you can cross-multiply the denominators of each fraction with the opposing numerator:

$\frac{4}{5}=\frac{3}{x}\phantom{\rule{0ex}{0ex}}5\left(3\right)=4x\phantom{\rule{0ex}{0ex}}15=4x\phantom{\rule{0ex}{0ex}}\frac{15}{4}=x\phantom{\rule{0ex}{0ex}}3.75=x\phantom{\rule{0ex}{0ex}}$

For more complicated proportions, such as the one below, you still use the same technique.

Solution

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To solve problems involving proportions, you need to know how to convert verbal statement to equations, first and foremost. To change sentences into mathematical expressions and equations, look for key words like these:

Increased: +

Sum: +

More: +

Decreased: –

Difference: –

Less: –

Twice: ×2

Doubled: ×2

Tripled: ×3

The same: =

The first example in the video below can be solved without knowing how to do this, but most questions in this question, including Example 2 does.