4 10 Adding and Subtracting Fractions Warm Up

4 -10 Adding and Subtracting Fractions Warm Up Problem of the Day Lesson Presentation Course 2

4 -10 Adding and Subtracting Fractions Bell Ringer 12 -06 Find the LCM for each set of numbers. 1. 8 and 12 2. 12 and 18 3. 10 and 12 4. 12 and 24 Course 2

4 -10 Adding and Subtracting Fractions Learn to add and subtract fractions. Course 2

4 -10 Adding and Subtracting Fractions From January 1 to March 14 of any given year, Earth completes approximately 1 of 5 its orbit around the Sun, while Venus completes approximately 1 its orbit. 3 The illustration shows what the 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. Course 2

4 -10 Adding and Subtracting Fractions Additional Example 1 A: Adding or Subtracting Fractions with Like Denominators Add. Write the answer in simplest form. A. 5 + 1 8 8 5+ 1 = 5 + 1 8 8 8 =6= 3 4 8 Course 2 Add the numerators and keep the denominator. Simplify.

4 -10 Adding and Subtracting Fractions Additional Example 1 B: Adding or Subtracting Fractions with Like Denominators Subtract. Write the answer in simplest form. B. 9 4 – 11 11 4 = 9– 4 9 – 11 11 11 = 5 11 Course 2 Subtract the numerators and keep the denominator. The answer is in the simplest form.

4 -10 Adding and Subtracting Fractions Additional Example 1 A: Adding or Subtracting Fractions with Like Denominators Add. Write the answer in simplest form. A. 5 + 1 6 6 5+ 1 = 5 + 1 6 6 6 =6= 1 6 Course 2 Add the numerators and keep the denominator. Simplify.

4 -10 Adding and Subtracting Fractions Additional Example 1 B: Adding or Subtracting Fractions with Like Denominators Subtract. Write the answer in simplest form. B. 7 4 – 10 10 4 = 7– 4 7 – 10 10 10 = 3 10 Course 2 Subtract the numerators and keep the denominator. The answer is in the simplest form.

4 -10 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 • Find the LCM (least common multiple) of the denominators. • Multiply the denominators. Helpful Hint The LCM of two denominators is the lowest common denominator (LCD) of the fractions. Course 2

4 -10 Adding and Subtracting Fractions Additional Example 2 A: Adding and Subtracting Fractions with Unlike Denominators Add. Write the answer in simplest form. A. 5 + 7 6 8 5 +7 = 5 · 4 + 7 · 3 The LCM of the denominator is 24. 6 8 6· 4 8· 3 Course 2 = 20 + 21 24 24 Write equivalent fractions using the common denominator. = 41 = 1 17 24 24 Divide.

4 -10 Adding and Subtracting Fractions Additional Example 2 B: Adding and Subtracting Fractions with Unlike Denominators Subtract. Write the answer in simplest form. B. 2 – 3 2– 3 Course 2 3 4 3 = 2 · 4– 3 · 3 4 3· 4 4· 3 = 8 – 9 12 12 1 =– 12 Multiply the denominators. Write equivalent fractions using the common denominator. Subtract.

4 -10 Adding and Subtracting Fractions Additional Example 2 C: Adding and Subtracting Fractions with Unlike Denominators Add. Write the answer in simplest form. C. – 2 + 1 7 3 – 2 + 1 = – 2 · 3 + 1 · 7 Multiply the denominators. 7 3 7· 3 3· 7 6 Write equivalent fractions using =– + 7 21 21 the common denominator. 1 = Add. 21 Course 2

4 -10 Adding and Subtracting Fractions Try This: Example 2 A Add. Write the answer in simplest form. A. 2 + 5 5 6 2 +5 = 2 · 6 + 5 · 5 Multiply the denominators. 5 6 5· 6 6· 5 Course 2 = 12 + 25 30 30 Write equivalent fractions using the common denominator. = 37 = 1 7 30 30 Divide.

4 -10 Adding and Subtracting Fractions Try This: Example 2 B Subtract. Write the answer in simplest form. B. 2 – 5 2– 5 Course 2 1 = 2 · 2– 1 · 5 2 5· 2 2· 5 = 4 – 5 10 10 1 – = 10 Multiply the denominators. Write equivalent fractions using the common denominator. Subtract.

4 -10 Adding and Subtracting Fractions Try This: Example 2 C Add. Write the answer in simplest form. C. – 3 + 1 5 2 – 3 + 1 = – 3 · 2 + 1 · 5 Multiply the denominators. 5 2 5· 2 2· 5 6 Write equivalent fractions using =– + 5 10 10 the common denominator. 1 =– Add. 10 Course 2

4 -10 Adding and Subtracting Fractions Additional Example 3: Astronomy Application 1 In one Earth year, Jupiter completes about 12 of its orbit around the Sun, while Mars completes about 1 of its orbit. How much more of its orbit 2 does Mars complete than Jupiter? The LCM of the 1– 1 = 1 · 6 – 1 · 1 denominators is 12. 2 12 12 · 1 2· 6 Write equivalent fractions = 6 – 1 12 12 using the common denominator. = 5 Subtract. 12 5 Mars completes 12 more of its orbit than Jupiter does. Course 2

4 -10 Adding and Subtracting Fractions Try This: Example 3 It takes Michelle 5 12 hour to drive to work. It takes Luke 1 hour to drive to work. 2 How much longer does it take Luke to drive to work? 1– 5 = 1 · 6 – 5 · 1 The LCM of the 2 12 12 · 1 denominators is 12. 2· 6 Write equivalent fractions = 6 – 5 12 12 using the common denominator. = 1 Subtract. 12 1 It takes Luke 12 hour longer to drive to work. Course 2

4 -10 Adding Insert Lesson and Subtracting Title Here. Fractions Exit Slip 12 -06 Add or subtract. Write each answer in simplest form. 2 1. 5 – 3 3 5 1 2. 8 + 8 11 3. 5 + 1 4. 7 12 7 7 2 12 1– 1 1 3 12 4 5. You need a nail to go through a 7 -inch door and 8 extend an extra 1 inch. How long should the nail 4 be? 1 1 in. 8 Course 2