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Example 1: Real-World Application English muffins come in packs of 8, and eggs come in cartons of 12. If there are 24 students, what is the least number of packs and cartons needed so that each student has a muffin sandwich with one egg and there are none left over?

The smallest number that is a multiple of two or more numbers is the least common multiple (LCM). In Additional Example 1, the LCM of 8 and 12 is 24. Vocabulary

Example 2: Using Multiples to Find the LCM Find the least common multiple (LCM). Method 1: Use a list. 4, 5, and 8

Example 3: Using Multiples to Find the LCM Find the least common multiple (LCM). Method 2: Use prime factorization. 6 and 20

Example 4: Using Multiples to Find the LCM Find the least common multiple (LCM). 15, 6, and 4

Check It Out: Example 5 Find the least common multiple (LCM). Method 2: Use a list. 3, 4, and 9

Check It Out: Example 6 Find the least common multiple (LCM). Method 3: Use prime factorization. 4 and 10

Fractions that represent the same value are equivalent. Remember! To add or subtract unlike fractions, first rewrite them as equivalent fractions with a common denominator. F.Y.I.

Example 7: Real-World Applications 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 __ Add +.

Example 8 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 __ Add +.

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. Vocabulary

Example 9: Adding and Subtracting Unlike Fractions Add or subtract. Write each answer in simplest form. Method 1: Multiplying denominators __ 3 8 –

Example 10: Adding and Subtracting Unlike Fractions Add or subtract. Write each answer in simplest form. Method 2: Use the LCD. – __ 3 8

Example 11: Adding and Subtracting Unlike Fractions Add or subtract. Write each answer in simplest form. Method 3: Use mental math __ 1 8 +

Example 12 Add or subtract. Write each answer in simplest form. Method 1: Multiplying denominators. – 8 10 __ 2 6