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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

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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.

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. Teacher 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.

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Subtract. Write the answer in simplest form. Teacher 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

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. Student Practice 1A: 5656 + 1616 5656 + 1616 = 5 + 1 6 Add the numerators and keep the common denominator. = 6666 = 1 Simplify.

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Subtract. Write the answer in simplest form. Student Practice 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

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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.

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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

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Subtract. Write the answer in simplest form. Teacher Example 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

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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 Teacher Example 2B: Adding and Subtracting Fractions with Unlike Denominators =+ 24 40 5 40 29 40

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. Teacher 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.

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Subtract. Write the answer in simplest form. Student Practice 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

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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 Student Practice 2B: =+ 5 10 6 10 11 10 = 1 1 10

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Add. Write the answer in simplest form. Student Practice 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

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Teacher 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

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Holt CA Course 1 4-2 Adding and Subtracting Fractions Student 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

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