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Adding & Subtracting Mixed Numbers

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Objective:. 7.1.02 To develop fluency in +, –, x, and ÷ of non-negative rational numbers. Essential Question: How can we add and subtract mixed numbers? Adding & Subtracting Mixed Numbers

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OLD Vocabulary: Mixed Number: the sum of a whole number and a fraction. Adding & Subtracting Mixed Numbers

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Real World: Carlos spent 2 2 / 5 hours on his math homework and 1 3 / 5 hours on his language arts homework. How much time did he spend doing both his math and science homework? Adding & Subtracting Mixed Numbers

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Rules: (1) Rewrite the Problem Vertically; (2) Add the Opposite; (3) Find LCD & Change Fractions; (4) Add/Subtract Fractions; (5) Add/Subtract Whole Numbers; (6) Check Sign & Simplify or Rename as necessary. Adding & Subtracting Mixed Numbers

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Example #1: Find 4 3 / 5 + 9 1 / 3 Adding & Subtracting Mixed Numbers

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Example #1: Find 4 3 / 5 + 9 1 / 3 3 5 1 3 + Adding & Subtracting Mixed Numbers 4 9

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Example #1: Find 4 3 / 5 + 9 1 / 3 3 x3 5 x3 1 x5 3 x5 = = Adding & Subtracting Mixed Numbers 4 9 +

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Example #1: Find 4 3 / 5 + 9 1 / 3 3 x3 9 5 x3 15 1 x5 5 3 x5 15 = = Adding & Subtracting Mixed Numbers 4 9 4 9 +

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Example #1: Find 4 3 / 5 + 9 1 / 3 3 x3 9 5 x3 15 1 x5 5 3 x5 15 14 15 = = + Adding & Subtracting Mixed Numbers 4 9 4 9 13 +

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Example #1: Find 4 3 / 5 + 9 1 / 3 3 x3 9 5 x3 15 1 x5 5 3 x5 15 14 15 = = + Adding & Subtracting Mixed Numbers 44 9 13 9 +

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Example #2: Find 10 2 / 3 – 2 1 / 6 Adding & Subtracting Mixed Numbers

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Example #2: Find 10 2 / 3 – 2 1 / 6 2 3 1 6 Adding & Subtracting Mixed Numbers 10 2 –

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Example #2: Find 10 2 / 3 – 2 1 / 6 2 x2 4 3 x2 6 1 1 6 6 = = Adding & Subtracting Mixed Numbers 10 2 –– 2

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Example #2: Find 10 2 / 3 – 2 1 / 6 2 x2 4 3 x2 6 1 1 6 6 3 6 = = Adding & Subtracting Mixed Numbers 10 2 2 8 ––

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Example #2: Find 10 2 / 3 – 2 1 / 6 2 x2 4 3 x2 6 1 1 6 6 3 1 6 2 = = Adding & Subtracting Mixed Numbers 10 2 2 8 –– = 8

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Example #3: Find 9 1 / 3 – 5 3 / 4 Adding & Subtracting Mixed Numbers

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Example #3: Find 9 1 / 3 – 5 3 / 4 1 3 4 Adding & Subtracting Mixed Numbers 9 5 –

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Example #3: Find 9 1 / 3 – 5 3 / 4 1 x4 3 x4 3 x3 4 x3 = = Adding & Subtracting Mixed Numbers 9 5 –

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Example #3: Find 9 1 / 3 – 5 3 / 4 1 x4 4 3 x4 12 3 x3 9 4 x3 12 = = Adding & Subtracting Mixed Numbers 9 5 9 5 ––

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Example #3: Find 9 1 / 3 – 5 3 / 4 1 x4 4 16 3 x4 12 12 3 x3 9 9 4 x3 12 12 = = Adding & Subtracting Mixed Numbers 9 5 9 5 –– = = 8 5 –

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Example #3: Find 9 1 / 3 – 5 3 / 4 1 x4 4 16 3 x4 12 12 3 x3 9 9 4 x3 12 12 7 12 = = Adding & Subtracting Mixed Numbers 9 5 9 5 3 –– = = 8 5 –

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Example #3: Find 9 1 / 3 – 5 3 / 4 1 x4 4 16 3 x4 12 12 3 x3 9 9 4 x3 12 12 7 12 = = Adding & Subtracting Mixed Numbers 9 5 9 5 3 –– = = 8 5 –

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Example #4: Find 15 3 / 7 + 7 5 / 6 Adding & Subtracting Mixed Numbers

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Example #4: Find 15 3 / 7 + 7 5 / 6 3 7 5 6 Adding & Subtracting Mixed Numbers 15 7 +

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Example #4: Find 15 3 / 7 + 7 5 / 6 3 x6 7 x6 5 x7 6 x7 = = Adding & Subtracting Mixed Numbers 15 7 +

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Example #4: Find 15 3 / 7 + 7 5 / 6 3 x6 18 7 x6 42 5 x7 35 6 x7 42 = = Adding & Subtracting Mixed Numbers 15 7 7 ++

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Example #4: Find 15 3 / 7 + 7 5 / 6 3 x6 18 7 x6 42 5 x7 35 6 x7 42 53 42 = = Adding & Subtracting Mixed Numbers 15 7 7 22 ++

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Example #4: Find 15 3 / 7 + 7 5 / 6 3 x6 18 7 x6 42 5 x7 35 6 x7 42 5311 4242 = = Adding & Subtracting Mixed Numbers 15 7 7 22 ++ = 23

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Example #4: Find 15 3 / 7 + 7 5 / 6 3 x6 18 7 x6 42 5 x7 35 6 x7 42 5311 4242 = = Adding & Subtracting Mixed Numbers 15 7 7 22 ++ = 23

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Example #5: Find 8 – 6 1 / 3 1 3 – 8 6 Adding & Subtracting Mixed Numbers

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Example #5: Find 8 – 6 1 / 3 3 1 1 3 3 – 8 6 6 7 – Adding & Subtracting Mixed Numbers We can rename 8 as 7 and 3/3

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Example #5: Find 8 – 6 1 / 3 3 1 1 3 3 2 3 – 8 1 6 6 7 – Adding & Subtracting Mixed Numbers

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Example #5: Find 8 – 6 1 / 3 3 1 1 3 3 2 3 – 8 1 6 6 7 – Adding & Subtracting Mixed Numbers

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Example #6: Find 2 1 / 8 – 3 2 / 3 1 8 2 3 Adding & Subtracting Mixed Numbers 2 3 –

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Example #6: Find 2 1 / 8 – 3 2 / 3 1 8 2 3 Adding & Subtracting Mixed Numbers 2 3 + –+ –

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Example #6: Find 2 1 / 8 – 3 2 / 3 1 x3 8 x3 2 x8 3 x8 = = Adding & Subtracting Mixed Numbers 2 3 + –+ –

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Example #6: Find 2 1 / 8 – 3 2 / 3 1 x3 3 8 x3 24 2 x8 16 3 x8 24 = = Adding & Subtracting Mixed Numbers 2 3 2 3 + –+ – + –+ –

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Example #6: Find 2 1 / 8 – 3 2 / 3 1 x3 3 16 8 x3 24 24 2 x8 16 3 3 x8 24 24 = = Adding & Subtracting Mixed Numbers 2 3 2 3 = = 3 2 – + –+ – + –+ –

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Example #6: Find 2 1 / 8 – 3 2 / 3 1 x3 3 16 8 x3 24 24 2 x8 16 3 3 x8 24 24 13 24 = = Adding & Subtracting Mixed Numbers 2 3 2 3 1 = = 3 2 – + –+ – + –+ –

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Example #6: Find 2 1 / 8 – 3 2 / 3 1 x3 3 16 8 x3 24 24 2 x8 16 3 3 x8 24 24 13 24 = = Adding & Subtracting Mixed Numbers 2 3 2 3 1 = = 3 2 – – + –+ – + –+ –

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Example #7: Find 2 1 / 4 – 3 2 / 5 Adding & Subtracting Mixed Numbers

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Example #7: Find 2 1 / 4 – 3 2 / 5 1 4 2 5 Adding & Subtracting Mixed Numbers 2 3 –

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Example #7: Find 2 1 / 4 – 3 2 / 5 1 4 2 5 Adding & Subtracting Mixed Numbers 2 3 + –+ –

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Example #7: Find 2 1 / 4 – 3 2 / 5 1 x5 5 16 4 x5 20 20 2 x4 8 3 5 x4 20 20 13 20 = = Adding & Subtracting Mixed Numbers 2 3 2 3 1 = = 3 2 – + –+ – + –+ –

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Example #6: Find 2 1 / 8 – 3 2 / 3 1 x3 3 16 8 x3 24 24 2 x8 16 3 3 x8 24 24 13 24 = = Adding & Subtracting Mixed Numbers 2 3 2 3 1 = = 3 2 – + –+ – + –+ –

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Real World: Kevin’s baby brother weighed 7 1 / 2 pounds at birth. After one month, his brother weighed 8 4 / 5 pounds. How much weight did the baby gain? Adding & Subtracting Mixed Numbers 1 3 / 10 lbs.

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Real World: Ms. Ivey plans to plant 4 7 / 8 acres of wheat and 1 2 / 3 acres of corn. How many acres of land does Mr. Ivey need altogether? Adding & Subtracting Mixed Numbers 6 13 / 24 acres of land

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Adding & Subtracting Mixed Numbers Rules: (1) Rewrite the Problem Vertically; (2) Add the Opposite; (3) Find LCD & Change Fractions; (4) Add/Subtract Fractions; (5) Add/Subtract Whole Numbers; (6) Check Sign & Simplify or Rename as necessary.

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HOMEWORK Adding & Subtracting Mixed Numbers

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