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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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

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

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

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

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?

​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