Finding Common Denominators

Finding Common Denominators

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Adding and Subtracting Fractions

We learned that in order to add or subtract fractions we need to have a common denominator

Adding and Subtracting Fractions

• Most have a common denominator

• Add or subtract numerators

• Simplify if necessary

Multiple Choice

Let's try a couple of questions. 

Solve.

 $-\frac{1}{8}+\frac{3}{8}$  

The answers have been simplified.

•  $-\frac{4}{8}=-\frac{1}{2}$  

•  $\frac{2}{8}=\frac{1}{4}$ 

•  $\frac{4}{8}=\frac{1}{2}$  

•  $-\frac{4}{16}=-\frac{1}{8}$  

Multiple Choice

Solve.

 $\frac{7}{11}-\left(-\frac{3}{11}\right)$  

•  $\frac{4}{11}$  

•  $-\frac{4}{11}$  

•  $\frac{10}{11}$  

•  $-\frac{10}{11}$  

Finding Common Denominators - 1st way

• Simply multiply the two denominators

• Multiply your first fraction by the 2nd fractions denominator

• Then multiply the second fraction by the 1st fractions denominator

• You will have two new equivalent fractions with common denominators.

Multiple Choice

Let's try! Use the image as an example. Find the common denominators and make an equivalent expression.

 $\frac{2}{3}+\frac{1}{4}$  

•  $\frac{2}{3}\cdot\frac{1}{4}+\frac{1}{4}\cdot\frac{2}{3}=\frac{2}{12}+\frac{2}{12}?$  

•  $\frac{2}{3}\cdot\frac{4}{4}+\frac{1}{4}\cdot\frac{3}{3}=\frac{8}{12}+\frac{3}{12}?$  

Another way to see it.

• Use sum of cross-multiplication

• Use product of denominators

• Simplify if necessary

Multiple Choice

Let's try again! Find the equivalent expression by finding the common denominators.

 $\frac{3}{7}+\frac{2}{3}$  

•  $\frac{3}{21}+\frac{2}{21}$  

•  $\frac{3}{10}+\frac{2}{10}$  

•  $\frac{9}{21}+\frac{14}{21}$  

Another way - Least Common Multiple (LCM)

• You find the least common multiple of each denominator

Let's make the denominators the same

Multiple Choice

Let's try finding the least common multiple first.

 $\frac{2}{5}+\frac{1}{4}$  
What is the least common multiple for 5 and 4?

• 60

• 20

• 9

• 40

Multiple Choice

Now that we know the least common multiple of 5 and 4 is 20. Let's make common denominators for

 $\frac{2}{5}+\frac{1}{4}$  

•  $\frac{2}{5}\cdot\frac{4}{4}=\frac{8}{20}\ and\ \frac{1}{4}\cdot\frac{5}{5}=\frac{5}{20}$  

•  $\frac{2}{5}\cdot\frac{1}{4}=\frac{2}{20}\ and\ \frac{1}{4}\cdot\frac{2}{5}=\ \frac{2}{20}$  

•  $\frac{2}{5}\cdot\frac{5}{5}=\frac{10}{25}\ and\ \frac{1}{4}\cdot\frac{4}{4}=\frac{4}{16}$  

Multiple Choice

Let's practice. Solve.

 $\frac{1}{2}+\frac{1}{4}$  

Remember, simplify if needed.

•  $\frac{3}{4}$  

•  $\frac{1}{3}$  

•  $\frac{2}{6}$  

Multiple Choice

Solve. Simplify, if needed.

 $\frac{1}{3}+\frac{1}{4}$  

•  $\frac{2}{12}$  

•  $\frac{1}{6}$  

•  $\frac{7}{12}$  

Multiple Choice

Solve. Pay attention to the integer. Simplify, if needed.

 $-\frac{2}{3}+\frac{1}{2}$  

•  $-\frac{1}{1}$  

•  $-\frac{1}{6}$  

•  $\frac{1}{6}$  

•  $-\frac{3}{5}$  

Multiple Choice

Solve. Pay attention to the integer. Simplify, if needed.

 $-\frac{1}{5}-\frac{1}{2}$  

•  $-\frac{2}{10}$  

•  $-\frac{3}{10}$  

•  $-\frac{7}{10}$  

•  $\frac{0}{10}$  

Homework

Complete pg. 60 and 61