Fraction Addition (with Models) Fraction addition requires a firm understanding of the meaning of a fraction’s numerator (the number of fractional parts at hand) and denominator (the number of fractional parts in the whole) as well as Addition facility in naming equivalent fractions. When adding two or more fractions with like denominators, the problem solver simply adds the numerators or the number of fractional parts in each addend. The denominator that shows the number of fractional parts in the whole does not change. When adding fractions that have unlike denominators, the problem solver must first rename the addends using a common denominator. Build Understanding Review the process of finding common multiples. Have students list a few multiples of 4 (4, 8, 12, 16, 20, 24) and 6 (6, 12, 18, 24, 30, 36). Then ask them to circle any numbers that are on both lists. Tell students that the circled numbers are common multiples of 4 and 6. If necessary, have students find common multiples of other number pairs, such as 4 and 10, 6 and 8, and 6 and 9. Using page 21, explain that when adding fractions with different denominators, students will need to find a common multiple of the denominators, or a common denominator. Then, they will rename these fractions using this common denominator. You may want to explain that renaming fractions will be easier if students use the smallest common denominator. Use questions like the following to guide students through the examples: • If you add fractions with the same denominator, what do you do to the numerators? (You add them.) What do you do to the denominator? (Nothing. It stays the same.) __1 __3 • In Example 2, what is a common denominator of 3 and 4 ? (12) Page 21 • To rename __1 with a denominator of 12, which number will you 3 Copyright © Wright Group/McGraw-Hill Answer Key multiply each part of the fraction by? (4, because 3 * 4 = 12) _6 • To rename __3 with a denominator of 12, which number will you 1. 7 4 multiply each part of the fraction by? (3, because 4 * 3 = 12) 3 _ Watch for students who add denominators. If it helps these 2. 4 Error Alert students, tell them to draw a diagram for each problem. This will help them 2 3. 1 _ see the denominator as the number of fractional parts in the whole. Also, 3 watch for students who have difficulty finding common denominators. Explain __7 to students that an easy way to find a common denominator of two fractions is 4. 12 to find the product of the two denominators. _5 5. 8 Check Understanding Divide the class into groups of 3 and ask each group to solve the problem _5 __1 + __2 6. 2 5 . Have one member of the group draw a diagram of the problem. Have 6 the other members use the algorithm. The group members then compare 17 their answers to make sure they are the same. If they are not the same, have 7. __ 24 the group members correct the error. When you are reasonably certain that most of your students understand the algorithm, assign the “Check Your __1 8. 1 24 Understanding ” exercises at the bottom of page 21. (See answers in margin.) 20 Teacher Notes EEM3_ALRH_PartM3_ALRH_Part 11_004-082_PDF.indd20_004-082_PDF.indd20 2200 99/15/08/15/08 22:44:50:44:50 PPMM PDF Pages Name Date Time Fraction Addition (with Models) Check that the addends have like denominators. Then add the numerators to find the sum. The denominator does not change. _1 _1 _3 Example 1 + 5 5 5 Addition _3 The denominators are the same. + 5 _4 Add the numerators. 5 _1 Example 2 3 _3 The denominators are not the same. + 4 _1 1____ ∗ 4 __4 Rename both fractions as = = equivalent fractions having 3 3 ∗ 4 12 a common denominator. _3 3____ ∗ 3 __9 + = = 4 4 ∗ 3 12 __13 12 _1 _3 __13 __1 Add the numerators. + = , or 3 4 12 112 Check Your Understanding Copyright © Wright Group/McGraw-Hill Solve the following problems. _4 _2 _1 _5 _5 _5 _1 _1 + + + + 1. 7 7 2. 8 8 3. 6 6 4. 3 4 _1 _1 _2 _1 _1 _3 _5 __5 + + + + 5. 2 8 6. 3 6 7. 3 8 8. 8 12 Write your answers on a separate sheet of paper. Student Practice 21 EEM3_ALRH_PartM3_ALRH_Part 11_004-082_PDF.indd21_004-082_PDF.indd21 2211 99/15/08/15/08 22:44:51:44:51 PPMM PDF Pages.