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**Fraction XI Adding Mixed Numbers With Unlike Denominators**

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**Some multiples of 3 & 4 12, 24, 36, 48, Common Multiple**

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

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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

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

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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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 =

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**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 =

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**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

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**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

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**Add These Mixed Numbers**

Use the short cut to find the Least Common Denominator (LCD). 1 10 3 6 1 3 + 6 6

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**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.

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**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

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**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

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**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

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**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

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

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**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

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**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

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**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

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**Add These Mixed Numbers**

Multiply across. 4 12 x 3 = 11 5 15 x 3 = 1 5 x 5 = 2 + 3 x 5 = 15

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**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

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**Change Your Improper Fraction to 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

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**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

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**Put Your Remainder Fraction Next 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

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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

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**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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