1. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers 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

2. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Add. Write the answer in simplest form. Example 1A: Adding Mixed Numbers 9 2323 + 12 2323 9 2323 + 2323 = 21 + 4343 Add the integers, and then add the fractions. = 21 + 1 1313 Rewrite the improper fraction as a mixed number. =22 1313 Add.

3. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Add. Write the answer in simplest form. Example 1B: Adding Mixed Numbers 5 1818 + 3 5656 5 1818 + 3 5656 Find a common denominator. = 8 + 23 24 = 8 23 24 Add the integers, and then add the fractions. Add. = 5 + 3 20 24 3 24

4. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Add. Write the answer in simplest form. Check It Out! Example 1B 4 1414 + 4 3838 4 1414 + 4 3838 Find a common denominator. = 8 + 5858 = 8 5858 Add the integers, and then add the fractions. Add. = 4 + 4 3838 2 8

5. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Sometimes when you subtract mixed numbers, the fraction portion of the first number is less than the fraction portion of the second number. In these cases, you must regroup before subtracting. REGROUPING MIXED NUMBERS WORDS NUMBERS 1818 7 = 6 + 1 + 1818 8888 = 6 + + 1818 = 6 9898 Rewrite 1 as a fraction with a common denominator. Regroup. Add.

6. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Remember! Any fraction in which the numerator and denominator are the same nonzero number is equal to 1.

7. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Example 2A: Subtracting Mixed Numbers Subtract. Write the answer in simplest form. 4 2323 – 2 1313 4 2323 – 2 1313 = Subtract the integers, and then subtract the fractions. 2 1313 + Add (combine integer and fraction. 1313 2

8. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Example 2B: Subtracting Mixed Numbers Subtract. Write the answer in simplest form. 12 8989 – 8 2323 8989 – 8 2323 = 8989 – 8 6969 Find a common denominator. = 4 2929 Subtract the integers, and then subtract the fractions.

9. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Subtract. Write the answer in simplest form. Example 2C: Subtracting Mixed Numbers 17 1818 – 12 3838 17 1818 – 12 = 3838 16 9898 – 12 3838 Regroup 17 1818 = 16+ 8888 + 1818. Subtract the integers, and then subtract the fractions. Simplify. = 4 6868 = 4 3434 WRITE THIS AT THE TOP OF YOUR PAGE BORROWING (regrouping)

10. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Check It Out! Example 2A Subtract. Write the answer in simplest form. 3 4545 – 2 1515 3 4545 – 2 1515 = Subtract the integers, and then subtract the fractions. 1 3535

11. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Check It Out! Example 2B Subtract. Write the answer in simplest form. 10 7878 – 4 3434 7878 – 4 3434 = 7878 – 4 6868 Find a common denominator. = 6 1818 Subtract the integers, and then subtract the fractions.

12. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Example 3: Measurement Application Kevin is 48 inches tall. His brother Keith is 5 3838 5858 inches taller. How tall is Keith? 48 3838 + 5 5858 = 53 8888 + Add the integers, and then add the fractions. = 53 + 1 Rewrite 8888 as 1. Keith is 54 inches tall. Estimate 48 1212 + 5 = 54 1212 Round 3838 to and to. 1212 1212 5858 54 equals 54, so the answer is reasonable.

13. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Add. Write the answer in simplest form. Check It Out! Example 1 7 4545 + 10 2525 7 4545 + 2525 = 17 + 6565 Add the integers, and then add the fractions. = 17 + 1 1515 Rewrite the improper fraction as a mixed number. =18 1515 Add.

14. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Subtract. Write the answer in simplest form. Check It Out! Example 2C 14 1414 – 10 3434 14 1414 – 10 = 3434 13 5454 – 10 3434 Regroup 14 1414 = 13+ 4444 + 1414. Subtract the integers, and then subtract the fractions. Simplify. = 3 2424 =3 1212

15. Holt CA Course 1 4-3 Adding and Subtracting Mixed Numbers Check It Out! Example 3 Alvin weighs 72 lbs. His baby brother weighs 15 lbs. How much do they weigh together? 72 2323 + 15 1313 = 87 3333 + Add the integers, and then add the fractions. = 87 + 1 Rewrite 3333 as 1. Together they weigh 88 pounds. 2323 1313 Estimate 73 + 15 = 88 2323 Round 72 to 73 and 15 to 15. 1313 88 equals 88, so the answer is reasonable.