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**Fraction X Adding Unlike Denominators**

By Monica Yuskaitis

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Reminder Be sure to do Fractions IX before continuing with this lesson.

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**Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42 Common Multiple**

A number that is a multiple of two or more numbers. Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42

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Least Common Multiple The smallest common multiple of a set of two or more numbers. 5 = 5, 10, 15, 20, 25, 30 6 = 6, 12, 18, 24, 30, 36

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**Shortcut for Finding the Least Common Denominator or Least Common Multiple**

Check to see if the smaller denominator divides evenly into the larger denominator. If it does, use the larger denominator for your LCD or LCM. 1 3 will divide evenly into 9, so 9 is your LCD or LCM. 3 1 + 9

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**To Add or Subtract Fractions With Unlike Denominators**

Find the multiples of each denominator. 1 5 = 5, 10, 15, 20, 25, 30 1 + 10 = 10, 20, 30, 40, 50

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**To Add or Subtract Fractions With Unlike Denominators**

Compare the lists of multiples. Circle the common multiples between the two lists. 1 5 = 5, 10, 15, 20, 25, 30 1 + 10 = 10, 20, 30, 40, 50

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**To Add or Subtract Fractions With Unlike Denominators**

Use the lowest common multiple as the denominator. 1 5 = 5, 10, 15 ,20 ,25 ,30 1 + 10 = 10, 20, 30, 40, 50

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**To Add or Subtract Fractions With Unlike Denominators**

This number is also called the least common denominator. 1 5 = 5, 10, 15 ,20 ,25 ,30 1 + 10 = 10, 20, 30, 40, 50

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**To Add or Subtract Fractions With Unlike Denominators**

Rewrite the fractions using the least common denominator or least common multiple. 1 5 10 1 + 10 10

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**To Add or Subtract Fractions With Unlike Denominators**

Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. You know that 1/10 is equal to 1/10 so Put a 1 over the Bottom 10. 1 5 10 1 1 + 10 10

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**To Add or Subtract Fractions With Unlike Denominators**

Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. To find the top number, ask yourself what do you multiply the 5 by to get 10. 1 5 10 1 1 + 10 10

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**To Add or Subtract Fractions With Unlike Denominators**

Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. That’s right 2. Since you are looking for the equivalent fraction you know the top number must also be multiplied by 2. 1 x 2 = 5 10 x 2 = 1 1 + 10 10

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**To Add or Subtract Fractions With Unlike Denominators**

Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. 1 2 x 2 = To find the top number just multiply 2 x 1 to get your equivalent fraction. 5 10 x 2 = 1 1 + 10 10

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**To Add or Subtract Fractions With Unlike Denominators**

Now just add the numerators. 1 2 x 2 = 5 10 x 2 = Remember when adding fractions you never add the denominators. 1 1 + 10 10 3 10

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**1 2 8 1 + 8 8 Add these Fractions Use the short cut to find the**

Least Common Denominator (LCD). 1 2 8 1 + 8 8

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**1 2 8 1 + 8 8 Add these Fractions x 4 = x 1 = Now find the equivalent**

fractions for 1/2 & 1/8. 1 2 8 x 4 = 1 + 8 x 1 = 8 Ask what do you multiply 2 by to get 8 and what do you multiply 8 by to get 8.

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**1 2 8 1 + 8 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =**

Since you are writing equivalent fractions, now multiply the top numbers by the same number you did in the bottom. 1 x 4 = 2 8 x 4 = 1 x 1 = + 8 x 1 = 8

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**1 4 2 8 1 1 + 8 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =**

Now multiply across. x 4 = 2 8 x 4 = 1 1 x 1 = + 8 x 1 = 8

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**1 4 2 8 1 1 + 8 8 5 8 Add these Fractions x 4 = x 4 = x 1 = x 1 =**

Add your new numerators. x 4 = 2 8 x 4 = 1 1 x 1 = + 8 x 1 = 8 5 8

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**2 5 15 1 + 3 15 Add these Fractions Find the common Multiples for**

5 and 3. Write This number As your new denominator. 2 5 15 1 + 3 15

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**2 5 15 1 + 3 15 Add these Fractions x 3 = x 5 = Ask yourself what you**

multiply the bottom number by to get 15. 2 5 15 x 3 = 1 + 3 x 5 = 15

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**2 5 15 1 + 3 15 Add these Fractions x 3 = x 3 = x 5 = x 5 =**

Multiply the top number by the same number you did in the bottom. 2 x 3 = 5 15 x 3 = 1 x 5 = + 3 x 5 = 15

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**2 6 5 15 1 5 + 3 15 Add these Fractions x 3 = x 3 = x 5 = x 5 =**

Multiply across. 2 6 x 3 = 5 15 x 3 = 1 5 x 5 = + 3 x 5 = 15

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**2 6 5 15 1 5 + 3 15 11 15 Add these Fractions x 3 = x 3 = x 5 = x 5 =**

Now add your new numerators. 2 6 x 3 = 5 15 x 3 = 1 5 x 5 = + 3 x 5 = 15 11 15

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Add these Fractions 1 2 x 2 = 6 12 x 2 = 1 3 x 3 = + 4 x 3 = 12 5 12

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Add these Fractions 5 20 x 4 = 6 24 x 4 = 1 3 x 3 = + 8 x 3 = 24 23 24

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Add these Fractions 2 6 x 3 = 3 9 x 3 = 1 1 x 1 = + 9 x 1 = 9 7 9

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**4 12 5 15 2 10 + 3 15 22 15 Add these Fractions x 3 = x 3 = x 5 =**

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Simplify Your Answer 7 1 15 22 15) 22 15 15 7

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Fraction IX Least Common Multiple Least Common Denominator

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