Learn to add and subtract fractions with unlike denominators.

Vocabulary least common denominator (LCD)‏

The Pacific Ocean covers of Earth’s surface. The Atlantic 1 3 __ The Pacific Ocean covers of Earth’s surface. The Atlantic Ocean covers of Earth’s surface. To find the fraction of Earth’s surface that is covered by both oceans, you can add and , which are unlike fractions. 1 5 __ 1 3 __ 1 5 __

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.

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? 1 4 __ 1 3 __ 1 4 __ 3 Add + . ? 1 4 __ 3 1 4 __ 1 3 __ + _____ Find a common denominator for 4 and 3: 4 x 3 = 12.

Additional Example 1 Continued 4 __ 3 12 __ Write equivalent fractions with 12 as the common denominator. 1 3 __ 4 12 __ Add the numerators. Keep the common denominator. + _______ _____ 7 12 __ 1 4 __ 1 3 __ 1 12 7 12 __ The pepperoni and onions cover of the pizza.

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? 1 3 __ 1 2 __ 1 3 __ 2 Add + . 1 3 __ 1 2 __ 1 3 __ ? 1 2 __ + Find a common denominator for 3 and 2: 3 X 2 = 6. _____

Check It Out: Example 1 Continued 3 __ 2 6 __ Write equivalent fractions with 6 as the common denominator. 1 2 __ 3 6 __ Add the numerators. Keep the common denominator. + _______ _____ 5 6 __ 1 3 __ 2 6 The peppers and ham cover of the pizza. 5 6 __

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.

Additional Example 2A: Adding and Subtracting Unlike Fractions Add or subtract. Write each answer in simplest form. Method 1: Multiplying denominators. 7 10 __ 3 8 __ – 7 10 __ 3 8 __ – Multiply the denominators. 10 • 8 = 80 56 80 __ 30 80 __ Write equivalent fractions with a common denominator. – 26 80 __ Subtract. 13 40 __ Write the answer in simplest form.

Additional Example 2B: Adding and Subtracting Unlike Fractions Add or subtract. Write each answer in simplest form. Method 2: Use the LCD. – 11 12 __ 3 8 __ Multiples of 12: 12, 24, … 11 12 __ 3 8 __ – Multiples of 8: 8, 16, 24, … The LCD is 24. 22 24 __ 9 24 __ – Write equivalent fractions with a common denominator. 13 24 __ Subtract.

Additional Example 2C: Adding and Subtracting Unlike Fractions Add or subtract. Write each answer in simplest form. Method 3: Use mental math. 5 16 __ 1 8 __ + 5 16 __ 1 8 __ Think: 16 is a multiple of 8, so the LCD is 16. + 5 16 __ 2 16 __ 1 8 __ + Rewrite with a denominator of 16. 7 16 __ Add.

Additional Example 2D: Adding and Subtracting Unlike Fractions Add or subtract. Write each answer in simplest form. Method 3: Use mental math. 5 16 __ 1 8 __ – 5 16 __ 1 8 __ Think: 16 is a multiple of 8, so the LCD is 16. – 5 16 __ 2 16 __ 1 8 __ – Rewrite with a denominator of 16. 3 16 __ Subtract.

Check It Out: Example 2A Add or subtract. Write each answer in simplest form. Method 1: Multiplying denominators. – 8 10 __ 2 6 __ 8 10 __ 2 6 __ – Multiply the denominators. 10 • 6 = 60 48 60 __ 20 60 __ – Write equivalent fractions with a common denominator. 28 60 __ Subtract. 7 15 __ Write the answer in simplest form.

Check It Out: Example 2B Add or subtract. Write each answer in simplest form. Method 2: Use the LCD. – 4 7 __ 1 3 __ Multiples of 7: 7, 14, 21, … 4 7 __ 1 3 __ – Multiples of 3: 3, 6, 9, 12, 15, 18, 21, … The LCD is 21. 12 21 __ 7 21 __ – Write equivalent fractions. 5 21 __ Subtract.

Check It Out: Example 2C Add or subtract. Write each answer in simplest form. Method 3: Use mental math. 3 12 __ 1 6 __ + 3 12 __ 1 6 __ Think: 12 is a multiple of 6, so the LCD is 12. + 3 12 __ 2 12 __ 1 6 __ + Rewrite with a denominator of 12. 5 12 __ Add.

Check It Out: Example 2D Add or subtract. Write each answer in simplest form. Method 3: Use mental math. 3 12 __ 1 6 __ – 3 12 __ 1 6 __ Think: 12 is a multiple of 6, so the LCD is 12. – 3 12 __ 2 12 __ 1 6 __ – Rewrite with a denominator of 12. 1 12 __ Subtract.