Adding & Subtracting Mixed Numbers

Objective: 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Example #3: Find 9 1 / 3 – 5 3 / 4 1 x x x x = = Adding & Subtracting Mixed Numbers –– = = 8 5 –

Example #3: Find 9 1 / 3 – 5 3 / 4 1 x x x x = = Adding & Subtracting Mixed Numbers –– = = 8 5 –

Example #3: Find 9 1 / 3 – 5 3 / 4 1 x x x x = = Adding & Subtracting Mixed Numbers –– = = 8 5 –

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

Example #4: Find 15 3 / / Adding & Subtracting Mixed Numbers

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

Example #4: Find 15 3 / / 6 3 x x x x7 42 = = Adding & Subtracting Mixed Numbers

Example #4: Find 15 3 / / 6 3 x x x x = = Adding & Subtracting Mixed Numbers

Example #4: Find 15 3 / / 6 3 x x x x = = Adding & Subtracting Mixed Numbers = 23

Example #4: Find 15 3 / / 6 3 x x x x = = Adding & Subtracting Mixed Numbers = 23

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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.

HOMEWORK Adding & Subtracting Mixed Numbers