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Learn to add and subtract fractions with unlike denominators, find common denominators, and simplify answers. Practice problems included for better understanding.
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Adding and Subtracting with Unlike Denominators 5-2 Course 1 Warm Up Problem of the Day Lesson Presentation
1 2 11 7 3 11 2 1 1 4 3 8 __ __ __ __ __ __ __ __ __ __ __ 7 7 15 15 9 20 20 9 7 15 4 Warm Up Add. Write each answer in simplest form. 1. + 2. + 3. + 4. +
Problem of the Day If it takes 12 minutes to cut a pipe into three pieces, how long would it take to cut the pipe into four pieces? 18 minutes
Learn to add and subtract fractions with unlike denominators.
Vocabulary least common denominator (LCD)
1 1 1 1 __ __ __ __ 3 3 5 5 The Pacific Ocean covers of Earth’s surface. The Atlantic Ocean covers of Earth’s surface. To find the fraction of the Earth’s surface that is covered by both oceans, you can add and , which are unlike fractions.
To add or subtract unlike fractions, first rewrite them as equivalent fractions with a common denominator. Remember! Fractions that represent the same value are equivalent.
1 1 1 1 1 1 1 1 __ __ __ __ __ __ __ __ 4 4 3 3 4 3 3 4 Add + . ? Additional Example 1: Cooking Application Mark made a pizza with pepperoni covering of the pizza and onions covering another . What fraction of the pizza is covered by pepperoni and onions? + Find a common denominator for 4 and 3. _____
1 7 1 7 1 1 3 4 __ __ __ __ __ __ __ __ 4 12 12 12 3 4 12 3 1 12 1 12 1 12 1 12 1 12 1 12 1 12 Additional Example 1 Continued Write equivalent fractions with 12 as the common denominator. Add the numerators. Keep the common denominator. + _______ _____ The pepperoni and onions cover of the pizza.
1 1 1 1 1 1 1 1 __ __ __ __ __ __ __ __ 2 3 2 3 3 2 2 3 Add + . Check It Out: Example 1 Tori made a pizza with peppers covering of the pizza and ham covering another . What fraction of the pizza is covered by ham and peppers? ? + Find a common denominator for 3 and 2. _____
1 1 1 5 2 1 3 __ __ __ __ __ __ __ 3 6 2 3 6 2 6 1 6 1 6 1 6 1 6 1 6 5 __ The peppers and ham cover of the pizza. 6 Check It Out: Example 1 Continued Write equivalent fractions with 6 as the common denominator. Add the numerators. Keep the common denominator. + _______ _____
You can use any common denominator or the least common denominator to add and subtract unlike fractions. The least common denominator (LCD) is the least common multiple of the denominators.
56 30 13 7 3 26 7 3 __ __ __ __ __ __ __ __ 8 80 10 40 8 10 80 80 Additional Example 2A: Adding and Subtracting Unlike Fractions Add or Subtract. Write each answer in simplest form. Method 1: Multiplying denominators. – – Multiply the denominators. 10 • 8 = 80 Write equivalent fractions with a common denominator. – Subtract. Write the answer in simplest form.
11 9 3 22 13 11 3 __ __ __ __ __ __ __ 24 24 8 12 8 12 24 Additional Example 2B: Adding and Subtracting Unlike Fractions Add or Subtract. Write each answer in simplest form. Method 2: Use the LCD. – Multiples of 12: 12, 24, … Multiples of 8: 8, 16, 24, … The LCD is 24. – Write equivalent fractions with a common denominator. – Subtract.
5 2 5 1 1 7 5 __ __ __ __ __ __ __ 16 16 16 16 8 16 8 1 __ 8 Additional Example 2C: Adding and Subtracting Unlike Fractions Add or Subtract. Write each answer in simplest form. Method 3: Use mental math. + Think: 16 is a multiple of 8, so the LCD is 16. + Rewrite with a denominator of 16. + Add.
5 2 5 1 1 3 5 __ __ __ __ __ __ __ 16 16 16 16 8 16 8 1 __ 8 Additional Example 2D: Adding and Subtracting Unlike Fractions Add or Subtract. Write each answer in simplest form. Method 3: Use mental math. – Think: 16 is a multiple of 8, so the LCD is 16. – – Rewrite with a denominator of 16. Subtract.
48 8 7 2 28 20 8 2 __ __ __ __ __ __ __ __ 6 60 60 6 60 15 10 10 Check It Out: Example 2A Add or Subtract. Write each answer in simplest form. Method 1: Multiplying denominators. – Multiply the denominators. 10 • 6 = 60 – Write equivalent fractions with a common denominator. – Subtract. Write the answer in simplest form.
4 7 1 12 5 4 1 __ __ __ __ __ __ __ 21 21 3 7 3 7 21 Check It Out: Example 2B Add or Subtract. Write each answer in simplest form. Method 2: Use the LCD. – Multiples of 7: 7, 14, 21, … – Multiples of 3: 3, 6, 9, 12, 15, 18, 21, …The LCD is 21. – Write equivalent fractions. Subtract.
3 2 3 1 1 1 3 __ __ __ __ __ __ __ 12 12 12 12 6 12 6 1 __ 6 Check It Out: Example 2D Add or Subtract. Write each answer in simplest form. Method 3: Use mental math. – Think: 12 is a multiple of 6, so the LCD is 12. – Rewrite with a denominator of 12. – Subtract.
1 1 1 3 5 5 1 1 3 1 13 3 1 7 1 __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 8 8 6 4 6 3 6 12 8 8 2 4 12 24 24 cup Lesson Quiz Add or subtract. Write each answer in simplest form. 1. + 2. – 3. – 4. + 5. Bonnie is making oatmeal bars and the recipes calls for cup of brown sugar. If she has cup of brown sugar, how much more does she need?
