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# Adding Fractions

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In this section, we learn how to add and subtract fractions. For this topic, we will have two different scenarios:

• Adding & Subtracting Fractions with a Common Denominator

• Adding & Subtracting Fractions without a Common Denominator

Adding & Subtracting Fractions with a Common Denominator:

-Place the result over the common denominator

$$\frac{6}{12}$$ -Simplify $$\frac{6}{12}=\frac{2 \cdot 3}{2 \cdot 2 \cdot 3}$$ $$\require{cancel}\frac{\cancel{2}\cdot \cancel{3}}{2 \cdot \cancel{2}\cdot \cancel{3}}=\frac{1}{2}$$ Adding & Subtracting Fractions without a Common Denominator:

Example 1: Find each difference $$\frac{1}{3}- \frac{2}{7}$$ -LCD = LCM(3,7)=21

-Rewrite each as an equivalent fraction with 21 as the denominator:

$$\frac{1}{3}\cdot \frac{7}{7}=\frac{7}{21}$$ $$\frac{2}{7}\cdot \frac{3}{3}=\frac{6}{21}$$ -Subtract the numerators: 7 - 6 = 1

-Place the result over the common denominator

$$\frac{1}{21}$$ -The fraction is already simplified $$\frac{1}{3}- \frac{2}{7}=\frac{1}{21}$$

• Adding & Subtracting Fractions with a Common Denominator

• Adding & Subtracting Fractions without a Common Denominator

Adding & Subtracting Fractions with a Common Denominator:

- Perform the given operation with the numerators - Add or Subtract the Numerators of the Fractions
- Place the result over the common denominator
- Simplify (reduce the fraction to lowest terms)

-Place the result over the common denominator

$$\frac{6}{12}$$ -Simplify $$\frac{6}{12}=\frac{2 \cdot 3}{2 \cdot 2 \cdot 3}$$ $$\require{cancel}\frac{\cancel{2}\cdot \cancel{3}}{2 \cdot \cancel{2}\cdot \cancel{3}}=\frac{1}{2}$$ Adding & Subtracting Fractions without a Common Denominator:

- Write equivalent fractions with the LCD as each denominator
- Perform the given operation with the numerators - Add or Subtract the Numerators of the Fractions
- Place the result over the common denominator
- Simplify (reduce the fraction to lowest terms)

Example 1: Find each difference $$\frac{1}{3}- \frac{2}{7}$$ -LCD = LCM(3,7)=21

-Rewrite each as an equivalent fraction with 21 as the denominator:

$$\frac{1}{3}\cdot \frac{7}{7}=\frac{7}{21}$$ $$\frac{2}{7}\cdot \frac{3}{3}=\frac{6}{21}$$ -Subtract the numerators: 7 - 6 = 1

-Place the result over the common denominator

$$\frac{1}{21}$$ -The fraction is already simplified $$\frac{1}{3}- \frac{2}{7}=\frac{1}{21}$$

Adding Fractions Resources:

Videos:

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

Math is Fun - Text Lesson AAA Math - Text Lesson Purple Math - Text Lesson Worksheets:

Super Teacher - Worksheet Khan Academy - Practice Khan Academy - Practice + Show More +