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EXAMPLE 1

EXAMPLE 1. Adding Mixed Numbers. Sports. Korey is training to compete in a race. What is the total distance he will run in the race?. 1. 1. 4. Find the sum. 2. +. 3. 3. 1. 1. 2. 3. 1. 4. +. 3. Add the fractions. Then add the whole numbers. 2. 6. 3. 2. ANSWER.

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EXAMPLE 1

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  1. EXAMPLE 1 Adding Mixed Numbers Sports Korey is training to compete in a race. What is the total distance he will run in the race?

  2. 1 1 4 Find the sum 2 + 3 3 1 1 2 3 1 4 + 3 Add the fractions. Then add the whole numbers. 2 6 3 2 ANSWER Korey will run miles in the race. 6 3 EXAMPLE 1 Adding Mixed Numbers SOLUTION

  3. 5 3 3 1 3. 2. 2 2 3 2 + + 11 5 11 5 8 5 4 ANSWER ANSWER ANSWER 5 4 4 11 9 5 for Example 1 GUIDED PRACTICE Find the sum. 1 4 1. 3 1 + 9 9

  4. 3 1 4. 1 2 + 7 7 4 ANSWER 3 7 for Example 1 GUIDED PRACTICE Find the sum.

  5. 3 . + Find the sum 1 4 1 2 1 1 12 = 2 2 12 12 3 9 3 3 , 12. 1 = 1 + + Rewrite using the LCD 12 4 4 3 5 10 , or 3 3 12 6 10 5 , . 3 ANSWER The sum is or 3 12 6 EXAMPLE 2 Simplifying Mixed Number Sums Add the fractions. Then add the whole numbers.Simplify.

  6. 3 9 3 1 7 4 1 1 + 7 8. + + 3 + 1 5 6. 3 7. 6 5. 4 3 10 5 4 8 5 9 3 4 19 1 9 10 20 8 7 4 9 1 The sum is ANSWER ANSWER ANSWER ANSWER 11 The sum is The sum is The sum is 2 for Example 2 GUIDED PRACTICE Find the sum. Simplify if possible.

  7. 2 1 3 2 EXAMPLE 3 Solving Addition Problems Sculpture 1 The base of a sculpture is feet tall. The sculpture is feet tall. How tall is the sculpture with the base? 2

  8. 3 2 You need to add and 2 6 3 1 3 = 1 1 2 3 Rewrite both fractions using the LCD, 4 1 3 6. 2 + 2 = 6 2 3 7 6 1 1 2 7 7 1 , . 3 3 1 3 Think of as or To simplify, write the sum as + + 6 6 6 1 . 4 6 ANSWER 1 The sculpture with the base is feet tall. 4 6 EXAMPLE 3 Solving Addition Problems SOLUTION Add the fractions. Then add the whole numbers.

  9. 1 1 3 3 5 4 1 7 12 ANSWER The clown while wearing stilts is feet tall. for Example 3 GUIDED PRACTICE 9. Circus Performers A clown isfeet tall while barefoot andfeet taller while wearing stilts. How tall is the clown while wearing stilts?

  10. 3 32 4 1 5 2 1 38 4 ANSWER You need to buy inches of trim. for Example 3 GUIDED PRACTICE GUIDED PRACTICE 10. Home Improvement You want to cover a length of inches and a length of inches with wood trim. How much trim do you need to buy in all ?

  11. 17 1 20 3 1 5 EXAMPLE 4 Subtracting Mixed Numbers Volcanoes Before it erupted in 1980, the height of the Mount St. Helens volcano was about miles. After the eruption, the height was about miles. What was the decrease in the height?

  12. 3 17 1 You need to find the difference 1 . – 20 5 17 17 = 1 1 20 20 12 3 3 4 , 20. = 1 Rewrite using the LCD 1 – – 5 20 4 5 1 5 or , 4 20 1 The decrease in the height was about mile. 4 EXAMPLE 4 Subtracting Mixed Numbers SOLUTION Subtract the fractions. Then subtract the whole numbers. Simplify. ANSWER

  13. 5 7 4 3 11 1 3 1 − − 13. 14. 10 4 6 2 = 8 12 4 9 9 6 3 7 9 2 − 12. 8 5 = 10 5 10 17 7 = 24 5 = 6 for Example 4 GUIDED PRACTICE 2 – 1 11. 3

  14. 1 You are ANSWER ft taller than your friend 6 for Example 4 GUIDED PRACTICE 3 11 feet tall and your friend is 15. HeightYou are 4 4 4 12 feet tall. How much taller are you than your friend?

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