Dividing Fractions Lesson

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In this section, we continue to learn about fractions. Our next step is to learn about Dividing fractions. How do we divide one fraction by another? In order to
divide fractions, we must first learn about taking the reciprocal of a number. To find the reciprocal of a number, we swap the numerator and the denominator.

Find the Reciprocal of the following: $$\frac{2}{7}$$ -To find the reciprocal, we swap the numerator and denominator

-2 will become the denominator

-7 will become the numerator

Our reciprocal is: $$\frac{7}{2}$$ When we divide fractions, we convert the problem into multiplication of the first fraction by the reciprocal of the second.

Dividing Fractions:

-Multiply the dividend by the reciprocal of the divisor $$\frac{3}{4} \cdot \frac{2}{9}$$ $$\require{cancel}\frac{\cancel{3}}{\cancel{2} \cdot 2} \cdot \frac{\cancel{2}}{\cancel{3} \cdot 3}$$ Result: $$\frac{1}{6}$$ $$\frac{3}{4} \div \frac{9}{2} = \frac{1}{6}$$

Find the Reciprocal of the following: $$\frac{2}{7}$$ -To find the reciprocal, we swap the numerator and denominator

-2 will become the denominator

-7 will become the numerator

Our reciprocal is: $$\frac{7}{2}$$ When we divide fractions, we convert the problem into multiplication of the first fraction by the reciprocal of the second.

Dividing Fractions:

- Simplify each fraction involved in the division
- Leave the dividend or left fraction unchanged
- Setup the multiplication of the dividend by the reciprocal of the divisor
- Cross cancel and find the product

-Multiply the dividend by the reciprocal of the divisor $$\frac{3}{4} \cdot \frac{2}{9}$$ $$\require{cancel}\frac{\cancel{3}}{\cancel{2} \cdot 2} \cdot \frac{\cancel{2}}{\cancel{3} \cdot 3}$$ Result: $$\frac{1}{6}$$ $$\frac{3}{4} \div \frac{9}{2} = \frac{1}{6}$$

Dividing Fractions Resources:

Videos:

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

Math is Fun - Text Lesson
Khan Academy - Text Lesson
Purple Math - Text Lesson
Worksheets:

Math-Aids - Worksheet
K5 Learning - Worksheet
Khan Academy - Practice
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