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Fraction XI Adding Mixed Numbers With Unlike Denominators

Learn how to add mixed numbers with different denominators easily using common multiples and equivalent fractions. This tutorial guides you step by step.

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Fraction XI Adding Mixed Numbers With Unlike Denominators

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  1. Fraction XIAdding Mixed Numbers With Unlike Denominators By Monica Yuskaitis

  2. Common Multiple • A number that is a multiple of two or more numbers. Some multiples of 3 & 4 12, 24, 36, 48,

  3. Least Common Multiple • The smallest common multiple of a set of two or more numbers. 4 = 4, 8, 12, 16, 20, 24, 28 5 = 5, 10, 15, 20, 25, 30

  4. Mixed Numbers • Mixed numbers are whole numbers and fractions together. 1 3 2

  5. 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 2 will divide evenly into 8, so 8 is your LCD or LCM. 2 1 1 + 8

  6. To Add Fractions Mixed Numbers With Unlike Denominators • Find the multiples of each denominator. 1 3 4 = 4, 8, 12, 16, 20, 30 1 1 + 10 = 10, 20, 30, 40, 50

  7. To Add Mixed Fractions With Unlike Denominators • Compare the lists of multiples. Circle the common multiples between the two lists. 1 3 4 = 4, 8, 12, 16, 20, 24 1 1 + = 10, 20, 30, 40, 50 10

  8. To Add Mixed Fractions With Unlike Denominators • Use the least common multiple as the denominator. 1 3 4 = 4, 8, 12, 16, 20, 24 1 1 + = 10, 20, 30, 40, 50 10

  9. To Add Mixed Fractions With Unlike Denominators • This number is also called the least common denominator. 1 3 4 = 4, 8, 12, 16, 20, 24 1 1 + = 10, 20, 30, 40, 50 10

  10. To Add Mixed Fractions With Unlike Denominators • Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator. Ask yourself what you multiply 4 by to get 20. 1 3 4 20 x 5 = 1 1 + 10 20

  11. To Add Mixed Fractions With Unlike Denominators • Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator. That’s right 5. Since you are looking for the equivalent fraction you know the top number must also be multiplied by 5. 1 x 5 = 3 4 20 x 5 = 1 1 + 10 20

  12. To Add Mixed Fractions With Unlike Denominators • Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator. 1 5 x 5 = To find the top number just multiply 1 x 5 to get your equivalent fraction. 3 4 20 x 5 = 1 1 + 10 20

  13. To Add Mixed Fractions With Unlike Denominators • Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator. 1 5 x 5 = Now ask what you multiply the 10 by to get 20. 3 4 20 x 5 = 1 1 + 10 20 x 2 =

  14. To Add Mixed Fractions With Unlike Denominators • Find the equivalent fractions for 1/4 & 1/10 with 20 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 5 x 5 = 3 4 20 x 5 = 1 2 x 2 = 1 + 10 20 x 2 =

  15. To Add Mixed Fractions With Unlike Denominators • Now just add the numerators. 1 5 x 5 = 3 4 20 x 5 = 1 2 x 2 = Remember! We never add the denominators. 1 + 10 20 x 2 = 7 20

  16. To Add Mixed Fractions With Unlike Denominators • Now add the whole numbers. 1 5 x 5 = 3 4 20 x 5 = 1 2 x 2 = 1 + 10 20 x 2 = 7 4 20

  17. Add These Mixed Numbers Use the short cut to find the Least Common Denominator (LCD). 1 10 3 6 1 3 + 6 6

  18. Add These Mixed Numbers Now find the equivalent fractions for 1/3 & 1/6. 1 10 3 6 x 2 = 1 3 + 6 x 1 = 6 Ask what do you multiply 3 by to get 6 and what do you multiply 6 by to get 6.

  19. Add These Mixed Numbers Since you are writing equivalent fractions, now multiply the top numbers by the same number you did in the bottom. 1 x 2 = 10 3 6 x 2 = 1 x 1 = 3 + 6 x 1 = 6

  20. Add These Mixed Numbers 1 2 Now multiply across. x 2 = 10 3 6 x 2 = 1 1 x 1 = 3 + 6 x 1 = 6

  21. Add These Mixed Numbers 1 2 Add your new numerators. x 2 = 10 3 6 x 2 = 1 1 x 1 = 3 + 6 x 1 = 6 3 6

  22. Add These Mixed Numbers 1 2 Add your whole numbers. x 2 = 10 3 6 x 2 = 1 1 x 1 = 3 + 6 x 1 = 6 3 13 6

  23. Simplify Your Answer 3 ÷ 3 1 13 13 = 6 ÷ 3 2

  24. Add These Mixed Numbers Find the common multiples for 5 and 3. Write this number as your new denominator. 4 11 5 15 1 2 + 3 15

  25. Add These Mixed Numbers Ask yourself what you multiply the bottom number by to get 15. 4 11 5 15 x 3 = 1 2 + 3 x 5 = 15

  26. Add These Mixed Numbers Multiply the top number by the same number you did in the bottom. 4 x 3 = 11 5 15 x 3 = 1 x 5 = 2 + 3 x 5 = 15

  27. Add These Mixed Numbers Multiply across. 4 12 x 3 = 11 5 15 x 3 = 1 5 x 5 = 2 + 3 x 5 = 15

  28. Add These Mixed Numbers Now add your new numerators. 4 12 x 3 = 11 5 15 x 3 = 1 5 x 5 = 2 + 3 x 5 = 15 17 15

  29. Change Your Improper Fractionto a Mixed Number 2 4 12 x 3 = 11 1 15 5 15 x 3 = 15) 17 1 5 x 5 = 2 15 + 3 x 5 = 15 2 17 15

  30. Add Your 1 to Your Whole Numbers 2 1 4 12 x 3 = 11 1 15 5 15 x 3 = 15) 17 1 5 x 5 = 2 15 + 3 x 5 = 15 2 17 14 15

  31. Put Your Remainder FractionNext to Your Answer 2 1 4 12 x 3 = 11 1 15 5 15 x 3 = 15) 17 1 5 x 5 = 2 15 + 3 x 5 = 15 2 2 17 14 15 15

  32. Your Final Answer Is 14 2/15 2 1 4 12 x 3 = 11 1 15 5 15 x 3 = 15) 17 1 5 x 5 = 2 15 + 3 x 5 = 15 2 2 17 14 15 15

  33. Add These Mixed Numbers 11 1 5 20 x 4 = 24 1 24 6 24 x 4 = 24) 35 5 15 x 3 = 3 24 + 8 x 3 = 24 11 11 35 28 24 24

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