Least Common Denominator

​Adding and subtracting fractions

(Including) LCM, GCF, Simplifying, and Converting

Multiply each number by x1, x2, x3 (etc) to determine MULTIPLES.

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Stop when you find the FIRST multiple they have in common.​

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Can use for creating common denominators.

​Least common multiple

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Fill in the Blanks

What is the LCM of 8 and 12?

Fill in the Blanks

What is the LCM of 5, 6, and 15?

You can find common denominators by finding the LCM of the denominators, or by multiplying by the opposite denominator.

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​NOTE: Multiplying by the opposite denominator makes simplifying your fractions more difficult.

finding a common denominator

Fill in the Blanks

What is a common denominator for these two fractions?

Use the LCM strategy to find out.

$\frac{2}{3}$  and $\frac{1}{6}$  

Fill in the Blanks

What is a common denominator for these two fractions?

Use the LCM strategy to find out.

$\frac{3}{4}$  and $\frac{7}{12}$  

We cannot add or subtract fractions with unlike denominators.

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You have to create a common denominator by finding the LCM of BOTH denominators.​

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• See LCM slide.

• See Finding Common Denominators slide​.

adding and subtracting fractions

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Find the LCD of the denominators.

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We see that 35 is the LCD of 5 and 7.​

step one

​Multiply your first fraction by a fraction equivalent to ONE.

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We multiply by 7/7 because that gives us our LCD of 35.​

step two

Multiply your second fraction by a fraction equivalent to ONE.

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We multiply by 5/5 because that gives us our LCD of 35.​

step three

Add/subtract ONLY the numerators, and leave the denominator ALONE!

step four

Fill in the Blanks

Add / subtract these two fractions.

Do not simplify or convert to a mixed number.

$\frac{3}{4}\ +\ \frac{7}{10}$  

Fill in the Blanks

Add / subtract these two fractions.

Do not simplify or convert to a mixed number.

$\frac{8}{9}\ -\ \frac{1}{3}$  

List out every number that can be multiplied to get the multiple (break apart the multiple into its teeny-tiny factor pieces).

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Find the BIGGEST factor the numbers have in common.​

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Use for simplifying fractions.

greatest common factor

Fill in the Blanks

Find the GCF of 12 and 21.

Fill in the Blanks

Find the GCF of 8, 24, and 16.

To simplify your final fraction sum/difference, find the GCF of both the numerator AND the denominator.

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Divide the numerator and the denominator by the GCF.​

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• ​See GCF slide.

​simplifying fractions

Fill in the Blanks

Simplify.

$\frac{18}{27}$  

Fill in the Blanks

Simplify.

$\frac{6}{15}$  

Complete 5 divided by 3.

The whole number in the quotient becomes your whole number in the mixed fraction.

The remainder becomes your new numerator.

THE DENOMINATOR REMAINS THE SAME.​

improper to mixed

Multiply the denominator by the whole number, then add the numerator. THIS IS YOUR NEW NUMERATOR.

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LEAVE THE DENOMINATOR THE SAME.​

​​Mixed to improper

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Open Ended

What's wrong with this final answer?

Fill in the Blanks

Convert to an improper fraction.

$5\ \frac{2}{3}$  

Fill in the Blanks

Convert to a mixed number. Simplify if necessary.

$\frac{14}{4}$  

​Practice: Adding and Subtracting Fractions

​show what you know

Complete the following practice questions on adding and subtracting fractions using the strategies we've just reviewed.

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You may use a white board, or complete your work inside your MSG.​

You can go back and look at the previous slides if you're having trouble.

Multiple Choice

3/6 + 1/2

• 4/8

• 1

• 5/6

• 2/3

Multiple Choice

$$2\frac{2}{3}\ -\ 1\ \frac{11}{12}$$  

• 3/4

• $$1\frac{9}{12}$$  

• $$1\ \frac{3}{12}$$  

• 1/4

Multiple Choice

8/9 - 2/6

• 4/9

• 6/3

• 5/9

• 1/3

Multiple Choice

Tommy has 1/2 a gallon of blue paint, 2/3 gallon of green paint, and 1/4 gallon of yellow paint. How much paint does Tommy have in all?

• $$1\ \frac{5}{12}$$  gallons

• 17/12 gallons

• 4/9 gallons

• 9/15 gallons