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hendricks_beginning_algebra_1e_ch1_3

�������������������� Finding the LCD Step 1: Write the prime factorization of each denominator. Step 2: For each of the different factors, circle the largest number of occurrences of this factor found in the factorizations. Step 3: The product of the circled factors is the LCD. ������������ The LCD must include all of the different factors found in the denominators. The factor must repeat the largest number of times it appears in any of the denominators. ���������������������� Adding or Subtracting Fractions with Unlike Denominators Step 1: Determine the LCD. Step 2: Convert each fraction to an equivalent fraction with the LCD as its denominator. Multiply the numerator and denominator by the number that is needed to make the denominator the LCD. Step 3: Add or subtract the fractions. Step 4: Simplify the result, if necessary. �� ������������������������ ������������������ Add or subtract the fractions and simplify the result. 7a. 2 3 + 1 4 7b. 5 12 - 3 8 7c. 2 + 5 6 7d. 4 1 12 - 1 9 14 2 3 Solutions 7a. + 1 4 = 2 3 · 4 4 + 1 4 · 3 3 = 8 12 + 3 12 Multiply each fraction by a form of 1 to obtain the LCD, 12. Simplify each product. = 8 + 3 12 Add the numerators and place over the common denominator. = 11 12 Simplify the numerator. 7b. The LCD of 12 and 8 can be found as follows. 12 = 2 · 2 · 3 8 = 2 · 2 ·2 LCD = 2 · 2 · 2 · 3 = 24 5 12 - 3 8 = 5 12 · 2 2 - 3 8 · 3 3 = 10 24 - 9 24 = 10 - 9 24 = 1 24 7c. 2 + 5 6 = 2 1 + 5 6 Multiply each fraction by a form of 1 to obtain the LCD, 24. Simplify each product. Subtract the numerators and place over the common denominator. Simplify the numerator. Write 2 as 2 1 . = 2 1 · 6 6 + 5 6 Multiply the fi rst fraction by a form of 1 to obtain the LCD, 6. 22 Chapter 1 Real Numbers and Algebraic Expressions


hendricks_beginning_algebra_1e_ch1_3
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