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Operations with mixed numbers to add or subtract

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Unformatted text preview: ne of the above 4. The fraction (A) (B) (C) (D) (E) 5. 2 4 6 8 9 432 can be simplified by dividing 801 numerator and denominator by 2. 3. The number 6,862,140 is divisible by I. 3 II. 4 III. 5 (A) I only (B) I and III only (C) II and III only (D) I, II, and III (E) III only www.petersons.com Operations with Fractions 27 4. OPERATIONS WITH MIXED NUMBERS To add or subtract mixed numbers, it is again important to find common denominators. If it is necessary to borrow in subtraction, you must borrow in terms of the common denominator. Example: 1 2 23 − 6 3 5 Solution: 1 5 23 = 23 3 15 2 6 −6 = −6 5 15 Since we cannot subtract 6 5 15 from , we borrow from 23 and rewrite our problem as 15 15 15 22 20 15 6 −6 15 14 . 15 In this form, subtraction is possible, giving us an answer of 16 Example: Add 17 Solution: 3 3 to 43 4 5 Again we first rename the fractions to have a common denominator. This time it will be 20. 3 15 17 = 17 4 20 3 12 +43 = +43 5 20 When adding, we get a sum of 60 27 7 , which we change to 61 . 20 20 To multiply or divide mixed numbers, always rename them as improper fractions first. Example: Multiply 3 ⋅ 1 ⋅ 2 Solution: 2 2 3 5 1 9 3 4 18 10 11 ⋅ ⋅ = 11 594 2 www.petersons.com 28 Chapter 2 Example: Divide 3 Solution: 2 3 5 by 5 4 8 15 45 15 8 2 ÷ = ⋅ = 4 45 3 4 8 3 Exercise 4 Work out each problem. Circle the letter that appears before your answer. 1. Find the sum of 1 , 2 (A) (B) (C) (D) (E) 2. 5 12 6 6 13 7 7 12 1 6 3 1 7 12 1 6 2 3 , and 3 . 3 4 4. Divide 17 (A) (B) (C) (D) (E) 1 4 1 by 70. 2 7 4 1 2 4 4 9 1 2 Subtract 45 (A) (B) (C) (D) (E) 7 15 12 5 15 12 7 16 12 5 16 12 5 17 12 5 from 61. 12 5. Find 1 (A) (B) (C) (D) 3 2 · 12 ÷ 8 . 4 5 2 5 5 288 1 2 5 1 2 1 2 2 3. Find the product of 32 (A) (B) (C) (D) (E) 26 13 169 1 10 2 160 7 1 1 and 5 . 2 5 (E) 160 www.petersons.com Operations with Fractions 29 5. COMPARING FRACTIONS There are two methods by which fractions may be compared to see which is larger (or smaller). Method I—Rename the fractions to have the same denominator. When this is done, the fracti...
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