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## Fraction X Adding Unlike Denominators

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**Fraction XAdding Unlike Denominators**By Monica Yuskaitis**Reminder**• Be sure to do Fractions IX before continuing with this lesson.**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**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**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**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**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**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**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**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**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**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**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**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**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**Add these Fractions**Use the short cut to find the Least Common Denominator (LCD). 1 2 8 1 + 8 8**Add these Fractions**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.**Add these Fractions**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**Add these Fractions**1 4 Now multiply across. x 4 = 2 8 x 4 = 1 1 x 1 = + 8 x 1 = 8**Add these Fractions**1 4 Add your new numerators. x 4 = 2 8 x 4 = 1 1 x 1 = + 8 x 1 = 8 5 8**Add these Fractions**Find the common Multiples for 5 and 3. Write This number As your new denominator. 2 5 15 1 + 3 15**Add these Fractions**Ask yourself what you multiply the bottom number by to get 15. 2 5 15 x 3 = 1 + 3 x 5 = 15**Add these Fractions**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**Add these Fractions**Multiply across. 2 6 x 3 = 5 15 x 3 = 1 5 x 5 = + 3 x 5 = 15**Add these Fractions**Now add your new numerators. 2 6 x 3 = 5 15 x 3 = 1 5 x 5 = + 3 x 5 = 15 11 15**Add these Fractions**1 2 x 2 = 6 12 x 2 = 1 3 x 3 = + 4 x 3 = 12 5 12**Add these Fractions**5 20 x 4 = 6 24 x 4 = 1 3 x 3 = + 8 x 3 = 24 23 24**Add these Fractions**2 6 x 3 = 3 9 x 3 = 1 1 x 1 = + 9 x 1 = 9 7 9**Add these Fractions**4 12 x 3 = 5 15 x 3 = 2 10 x 5 = + 3 x 5 = 15 22 15**Simplify Your Answer**7 1 15 22 15) 22 15 15 7