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## 4-10

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**Adding and Subtracting Fractions**4-10 Course 2 Warm Up Problem of the Day Lesson Presentation**Adding and Subtracting Fractions**4-10 Course 2 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**Adding and Subtracting Fractions**4-10 5 9 7 60 + 306 + 42 + + = = 1 408 34 12 38 Course 2 Problem of the Day Let A through l represent digits of a number. Replace the letters A through l with the digits 1 through 9, respectively, and verify that the statement is true. ( ) ( ) E CD ( ) AB l G = 1 + + FH**Adding and Subtracting Fractions**4-10 Course 2 Learn to add and subtract fractions.**Adding and Subtracting Fractions**4-10 From January 1 to March 14 of any given year, Earth completes approximately of its orbit around the Sun, while Venus completes approximately its orbit. 1 5 1 3 Course 2 The illustration shows whatthe positions of the planets would be on March 14 if they started at the same place on January 1 and their orbits were circular. To find out how much more of its orbit Venus completes than Earth, you need to subtract fractions.**Adding and Subtracting Fractions**4-10 Course 2 Additional Example 1A: Adding or Subtracting Fractions with Like Denominators Add. Write the answer in simplest form. 5 8 1 8 A. + 5 + 1 5 8 1 8 Add the numerators and keep the denominator. + = 8 3 4 6 8 = = Simplify.**Adding and Subtracting Fractions**4-10 5 11 = Course 2 Additional Example 1B: Adding or Subtracting Fractions with Like Denominators Subtract. Write the answer in simplest form. 9 11 4 11 B. – Subtract the numerators and keep the denominator. 4 11 9 11 9 – 4 = – 11 The answer is in the simplest form.**Adding and Subtracting Fractions**4-10 Course 2 Additional Example 1A: Adding or Subtracting Fractions with Like Denominators Add. Write the answer in simplest form. 5 6 1 6 A. + 5 + 1 5 6 1 6 Add the numerators and keep the denominator. + = 6 6 6 1 = = Simplify.**Adding and Subtracting Fractions**4-10 3 10 = Course 2 Additional Example 1B: Adding or Subtracting Fractions with Like Denominators Subtract. Write the answer in simplest form. 7 10 4 10 B. – Subtract the numerators and keep the denominator. 4 10 7 10 7 – 4 = – 10 The answer is in the simplest form.**Adding and Subtracting Fractions**4-10 Helpful Hint The LCM of two denominators is the lowest common denominator (LCD) of the fractions. Course 2 To add or subtract fractions with different denominators, you must rewrite the fractions with a common denominator**Adding and Subtracting Fractions**4-10 Course 2 Additional Example 2A: Adding and Subtracting Fractions with Unlike Denominators Add. Write the answer in simplest form. 5 6 7 8 + A. 5 · 4 6 · 4 7 · 3 8 · 3 5 6 7 8 = + The LCM of the denominator is 24. + 21 24 20 24 Write equivalent fractions using the common denominator. = + 41 24 17 24 = = Divide. 1**Adding and Subtracting Fractions**4-10 8 12 9 12 – = 1 12 =– Course 2 Additional Example 2B: Adding and Subtracting Fractions with Unlike Denominators Subtract. Write the answer in simplest form. 3 4 2 3 B. – 3 · 3 2 · 4 2 3 3 4 – – = Multiply the denominators. 3 · 4 4 · 3 Write equivalent fractions using the common denominator. Subtract.**Adding and Subtracting Fractions**4-10 2 7 1 3 1 · 7 3 · 7 2 · 3 7 · 3 + – = – + 6 21 7 21 = + – 1 21 Course 2 Additional Example 2C: Adding and Subtracting Fractions with Unlike Denominators Add. Write the answer in simplest form. 2 7 1 3 C. – + Multiply the denominators. Write equivalent fractions using the common denominator. = Add.**Adding and Subtracting Fractions**4-10 Course 2 Try This: Example 2A Add. Write the answer in simplest form. 2 5 5 6 + A. 2 · 6 5 · 6 5 · 5 6 · 5 2 5 5 6 = + Multiply the denominators. + 25 30 12 30 Write equivalent fractions using the common denominator. = + 37 30 7 30 = = Divide. 1**Adding and Subtracting Fractions**4-10 4 10 5 10 – = 1 10 = Course 2 Try This: Example 2B Subtract. Write the answer in simplest form. 1 2 2 5 B. – 1 · 5 2 · 2 2 5 1 2 – – = Multiply the denominators. 5 · 2 2 · 5 Write equivalent fractions using the common denominator. Subtract. –**Adding and Subtracting Fractions**4-10 3 5 1 2 1 · 5 2 · 5 3 · 2 5 · 2 + – = – + 6 10 5 10 = + – 1 10 Course 2 Try This: Example 2C Add. Write the answer in simplest form. 3 5 1 2 C. – + Multiply the denominators. Write equivalent fractions using the common denominator. = – Add.**Adding and Subtracting Fractions**4-10 In one Earth year, Jupiter completes about of itsorbit around the Sun, while Mars completes about of its orbit. How much more of its orbit does Mars complete than Jupiter? 1 2 1 12 1 12 1 2 1 · 6 1 · 1 12 · 1 – – = 2 · 6 1 12 6 12 = – 5 12 = 5 12 Mars completes more of its orbit than Jupiter does. Course 2 Additional Example 3: Astronomy Application The LCM of the denominators is 12. Write equivalent fractions using the common denominator. Subtract.**Adding and Subtracting Fractions**4-10 5 12 5 12 1 2 1 · 6 5 · 1 12 · 1 – – = 2 · 6 5 12 6 12 = – 1 12 = 1 12 It takes Luke hour longer to drive to work. Course 2 Try This: Example 3 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? 1 2 The LCM of the denominators is 12. Write equivalent fractions using the common denominator. Subtract.**Adding and Subtracting Fractions**4-10 1 8 1 in. Course 2 Insert Lesson Title Here Lesson Quiz Add or subtract. Write each answer in simplest form. 3 8 2 7 5 8 5 7 3 7 + 1 1. – 2. 1 12 11 12 1 3 5 12 1 2 1 4 + 4. – 3. 7 8 5. You need a nail to go through a -inch door and extend an extra inch. How long should the nail be? 1 4