# HOW TO ADD AND SUBTRACT MIXED NUMBERS

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1 WHAT'S THAT MEAN...? HOW TO ADD AND SUBTRACT MIXED NUMBERS 8 2/3 1 1/4 5 TWO METHODS THAT WORK!! 1

2 Method 1: Use Improper Fractions What size parts are the circles cut into? How many yellow parts are on each side of the +? 4 4 How many 4ths in all? >> 4 4 << How many wholes and remaining parts? 2

3 Let's try Method 1 again! Use Improper Fractions without models... THE PROBLEM>>> Step A: Convert to improper fractions Step B: Add numerators & keep denominator. Step C: Convert to mixed number. 4 2/10 2 3/

4 Method 2: Use Mixed Numbers What size parts are the circles cut into? How many whole circles and how many parts are yellow on each side of the +? Add whole numbers 1st than fractions. Put it all back together as a 4 4

5 Let's try Method 2 again! Use Mixed Numbers without models... THE PROBLEM>>> 4 2/10 2 3/10 Step A: Add the whole numbers first Step B: Add the fractions next. Step C: Add everything together /10 3/10 6 5/

6 Method 1: Use Improper Fractions A. Convert to improper fractions. B. Add numerators & keep denominators. C. Convert to ADDITION LIKE-DENOMINATOR RE-CAP! Method 2: Use Mixed Numbers A. Add the whole numbers first. B. Add fraction numerators & keep denominator. C. Combine everything together. 6

7 Method 1: Use Improper Fractions to subtract What fraction parts are the bars cut into? How many parts are blue on each side of the? Take away the parts of the 2nd fraction. <<Convert back to 7

8 Method 2: Subtract using Mixed Numbers What fraction parts are the bars cut into? How many whole bars and how many parts are blue on each side of the? 1st Whole # take away 2nd whole # 1st Numerator take away 2nd numerator 8

9 Method 1: Subtract using Improper fractions 4 5/6 2 1/6 = Step A: Convert to improper fractions. Step B: Subtract numerators. Step C: Convert back to a 4 x x = = 6 = 2 4/6 = 2 2/3 9

10 Method 2: Subtract using Mixed Numbers Step A: Subtract whole numbers and subtract fractions /6 2 1/6 = Step B: Combine results to a Step C: Simplify if needed = 2 4/ /6 = 2 2/3 10

11 Method 1: Use Improper Fractions A. Convert to improper fractions. B. Subtract numerators & keep denominators. C. Convert to LIKE-DENOMINATOR SUBTRACTION RE-CAP! Method 2: Use Mixed Numbers All of these problems had like denominators. A. Subtract the whole numbers first. B. Subtract fraction numerators & keep denominator. C. Keep as What if the denominators are unlike??? 11

12 22 or or How can you add or subtract when pieces are different sizes 12

13 Method 1: Use improper fractions. THE PROBLEM>>> 1 4/ /3 Follow these steps: A. Convert to improper fractions. B. Find least common denominator. C. Add numerators & keep denominators. D. Convert to x 3 = 27 8 x 5 = 40 5 x 3 = 15 3 x 5 = = / 15 4 r 7 7 = =

14 PRACTICE Method 1: Use improper fractions to add. 4 1/ /5 STEPS: A. Convert to improper fractions. B. Find least common denominator. C. Add numerators & keep denominators. D. Convert to 14

15 PRACTICE Method 1: Use improper fractions to subtract. 4 2/3 3 1/5 STEPS: A. Convert to improper fractions. B. Find least common denominator. C. Subtract numerators & keep denominators. D. Convert to 15

16 Method 2: Use Mixed Numbers. THE PROBLEM>>> 3 1/2 2 1/3 Follow these steps: A. Subtract whole numbers first. B. Find least common denominator of fractions. C. Subtract numerators & keep denominators. D. Put whole number and fraction back together. 3 2 = 1 1 x 3 = 3 1 x 2 = 2 2 x 3 = 6 3 x 2 = = /6 = 16

17 PRACTICE Method 2: Use mixed numbers to subtract. 5 3/4 2 1/3 STEPS: A. Subtract whole numbers first. B. Find least common denominator of fractions. C. Subtract numerators & keep denominators. D. Keep answer as a 17

18 PRACTICE Method 2: Use mixed numbers to add. 2 1/ /8 STEPS: A. Add whole numbers first. B. Find least common denominator of fractions. C. Add numerators & keep denominators. D. Keep answer as a 18

19 What do you have to remember to do when adding or subtracting mixed numbers with unlike denominators??? Does it matter which method you use for adding or subtracting? Explain. 19

20 PRACTICE PROBLEMS USE METHOD 1 OR 2 (Remember to find a common denominator and be sure to watch the signs!) 1 1 2/ /9 = 2 4 3/4-2 3/8 = 5 1/3-3 1/4 = 6 2/ /2 =

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