•Students rewrite and solve equations that are not obviously linear equations using properties of equality.
Lesson 8 Summary•Proportions are linear equations in disguise and are solved the same way we normally solve proportions.
•When multiplying a fraction with more than one term in the numerator and/or denominator by a number, put the
expressions with more than one term in parentheses so you remember to use the distributive property when
transforming the equation.
NYS Math Module 4 Grade 8 Lesson 8 Classwork and Examples
Concept Development
Some linear equations may not look like linear equations upon first glance. A simple example that you should
recognize is
x/5 = 6/12
What do we call this kind of problem and how do we solve it?
Theorem. Given rational numbers A, B, C, and D, so that B ≠ 0 and D ≠ 0, the property states
If A/B = C/D, then AD = BC.
Example 1 - Example 4: Given a linear equation in disguise, we will try to solve it.
Example 5:
In the diagram below, △ABC ∼ △A'B'C'. Using what we know about similar triangles, we can determine the value of x.
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
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