Proportion Definition Test #3

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In this section, we learn how to determine if two ratios or two rates represent a proportion. We start with determining
if two fractions are equal in value. To do this, we utilize a procedure known as the "equality test for fractions". This tells
us that if two fractions are equal in value, their cross products must be equal. What are cross products? Cross products occur when we multiply
across fractions, the denominator of one fraction is multiplied by the numerator of the other.

Example 1: Find the cross products $$\frac{3}{5}, \frac{1}{2}$$ • Multiply 2 x 3 = 6

• Multiply 5 x 1 = 5

The cross products here are 6 and 5.

Once we have mastered this concept, we apply the same logic to working with ratios and rates. To determine if two ratios or two rates represent a proportion, we simply check to see if their cross products are equal. We only think about the number parts, we do not look at the units. In the case of a rate, we must ensure that the same units are in the numerator and denominator of each.

Example 2: Determine if the following represents a proportion $$\frac{2}{3} = \frac{6}{9}$$ • The cross products are: 3 x 6 = 18 and 9 x 2 = 18

Since the cross products are equal, we do have a proportion

Example 1: Find the cross products $$\frac{3}{5}, \frac{1}{2}$$ • Multiply 2 x 3 = 6

• Multiply 5 x 1 = 5

The cross products here are 6 and 5.

Once we have mastered this concept, we apply the same logic to working with ratios and rates. To determine if two ratios or two rates represent a proportion, we simply check to see if their cross products are equal. We only think about the number parts, we do not look at the units. In the case of a rate, we must ensure that the same units are in the numerator and denominator of each.

Example 2: Determine if the following represents a proportion $$\frac{2}{3} = \frac{6}{9}$$ • The cross products are: 3 x 6 = 18 and 9 x 2 = 18

Since the cross products are equal, we do have a proportion

Proportion Definition Resources:

Videos:

Khan Academy - Video
Virtual Nerd - Video
Math Antics - Video
Text Lessons:

Math is Fun - Text Lesson
Soft Schools - Text Lesson
Purple Math - Text Lesson
Worksheets:

Teach-Nology - Worksheet
Math-Aids - Worksheet
Khan Academy - Practice
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