1. Holt CA Course 1 4-2 Adding and Subtracting Fractions Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Holt CA Course 1 4-2 Adding and Subtracting Fractions Warm Up Find the LCM for each set of numbers. 1. 8 and 12 2. 12 and 18 3. 10 and 12 4. 12 and 24 24 36 60 24

3. Holt CA Course 1 4-2 Adding and Subtracting Fractions NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. Also covered: NS2.4 California Standards

4. Holt CA Course 1 4-2 Adding and Subtracting Fractions To add and subtract fractions with like denominators, add or subtract the numerators and keep the common denominator.

5. Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. Additional Example 1A: Adding and Subtracting Fractions with Like Denominators 5858 + 1818 5858 + 1818 = 5 + 1 8 Add the numerators and keep the common denominator. = 6868 = 3434 Simplify.

6. Holt CA Course 1 4-2 Adding and Subtracting Fractions Subtract. Write the answer in simplest form. Additional Example 1B: Adding and Subtracting Fractions with Like Denominators 9 11 – 4 11 9 11 – 4 11 = 9 – 4 11 Subtract the numerators and keep the common denominator. The answer is in the simplest form. = 5 11

7. Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. Check It Out! Example 1A 5656 + 1616 5656 + 1616 = 5 + 1 6 Add the numerators and keep the common denominator. = 6666 = 1 Simplify.

8. Holt CA Course 1 4-2 Adding and Subtracting Fractions Subtract. Write the answer in simplest form. Check It Out! Example 1B 7 10 – 4 10 7 10 – 4 10 = 7 – 4 10 Subtract the numerators and keep the common denominator. The answer is in the simplest form. = 3 10

9. Holt CA Course 1 4-2 Adding and Subtracting Fractions To add or subtract fractions with different denominators, you must rewrite the fractions with a common denominator. Two Ways to Find a Common Denominator Method 1: Multiply the denominators. Method 2: Find the LCM (least common multiple) of the denominators.

10. Holt CA Course 1 4-2 Adding and Subtracting Fractions The LCM of two denominators is the least common denominator (LCD) of the fractions. Helpful Hint

11. Holt CA Course 1 4-2 Adding and Subtracting Fractions Subtract. Write the answer in simplest form. Additional Example 2A: Adding and Subtracting Fractions with Unlike Denominators 3434 – 2323 3434 – 2323 = 3  3 4  3 – 2  4 3  4 Use Method 1: Multiply the denominators. Write equivalent fractions using a common denominator. Subtract. = 9 12 – 8 12 = 1 12

12. Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. 1818 + 3535 Use Method 2: The LCM of the denominators is 40. Write equivalent fractions using a common denominator. = Add. 1818 + 3535 = 1  5 8  5 + 3  8 5  8 Additional Example 2B: Adding and Subtracting Fractions with Unlike Denominators =+ 24 40 5 40 29 40

13. Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. Additional Example 2C: Adding and Subtracting Fractions with Unlike Denominators 5656 + 7878 5656 + 7878 = 5  4 6  4 + 7  3 8  3 Use Method 2: The LCM of the denominators is 24. = 20 24 + 21 24 Write equivalent fractions using a common denominator. = 41 24 = 1 17 24 Add. Then simplify.

14. Holt CA Course 1 4-2 Adding and Subtracting Fractions Subtract. Write the answer in simplest form. Check It Out! Example 2A 3535 – 1212 3535 – 1212 = 3  2 5  2 – 1  5 2  5 Use Method 1: Multiply the denominators. Write equivalent fractions using a common denominator. Subtract. = 6 10 – 5 10 = 1 10

15. Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. 3535 + 1212 Use Method 1: Multiply the denominators. Write equivalent fractions using a common denominator. = Add. Then simplify. 3535 + 1212 = 3  2 5  2 + 1  5 2  5 Check It Out! Example 2B =+ 5 10 6 10 11 10 = 1 1 10

16. Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. Check It Out! Example 2C 2525 + 5656 2525 + 5656 = 2  6 5  6 + 5  5 6  5 Use Method 2: The LCM of the denominators is 30. = 12 30 + 25 30 Write equivalent fractions using a common denominator. = 37 30 Add. Then simplify. = 1 7 30

17. Holt CA Course 1 4-2 Adding and Subtracting Fractions Additional Example 3: Astronomy Application 1  6 2  6 – 1  1 12  1 Use Method 2: The LCM of the denominators is 12. Write equivalent fractions using a common denominator. Subtract. 1212 – = 1 12 = 6 12 – 1 12 = 5 12 In one Earth year, Jupiter completes about of its orbit around the Sun, while Mars completes about of its orbit. How much more of its orbit does Mars complete than Jupiter? 1212 1 12 Mars completes more of its orbit than Jupiter does. 5 12

18. Holt CA Course 1 4-2 Adding and Subtracting Fractions Check It Out! Example 3 1  6 2  6 – 5  1 12  1 The LCM of the denominators is 12. Write equivalent fractions using a common denominator. Subtract. 1212 – = 5 12 = 6 12 – 5 12 = 1 12 It takes Michelle hour to drive to work. It takes Luke hour to drive to work. How much longer does it take Luke to drive to work? 1212 5 12 It takes Luke hour longer to drive to work. 1 12

19. Holt CA Course 1 4-2 Adding and Subtracting Fractions Lesson Quiz Add or subtract. Write each answer in simplest form. 1 12 1313 2. 3838 + 5858 1. 5757 – 3737 3. 4. 1212 – 1414 5. You need a nail to go through a -inch door and extend an extra inch. How long should the nail be? 7 778778 1 in. 1 1818 2727 + 5 12 11 121 114114