24 Chapter 1 Real Numbers and Algebraic Expressions 8b. Simplify 4 9 + 1 9 . �������������������������������������� ���������������������������������������������������������������� 4 9 1 9 = 4 + 1 9 + 9 = 5 18 To add fractions with the same denominator, we add their numerators and place this sum over the common denominator. 4 9 + 1 9 = 4 + 1 9 = 5 9 + ANSWERS TO STUDENT CHECKS Student Check 1 a. 24 = 2 · 2 · 2 · 3 b. 128 = 2 · 2 · 2 · 2 · 2 · 2 · 2 Student Check 2 a. 39 50 b. 103,000 1,563,000 5 8 Student Check 3 a. b. 9 10 c. 1 6 15 56 Student Check 4 a. b. 10 21 c. 3 SUMMARY OF KEY CONCEPTS 16 25 Student Check 5 a. b. 1 14 c. 51 37 6 5 Student Check 6 a. b. 1 2 c. 3 5 d. 16 9 or 1 7 9 13 21 Student Check 7 a. b. 7 40 c. 22 3 d. 139 80 or 1 59 80 1. The prime factorization of a number is a way to write a number as a product of prime numbers. Prime numbers are 2, 3, 5, 7, 11, 13, and so on. 2. A fraction represents a part of a whole and is written as a b . 3. Fractions can be simplified by dividing the numerator and denominator by their common factor. 4. Multiply fractions by multiplying their numerators and their denominators together. 5. Divide fractions by multiplying by the reciprocal. The reciprocal of the fraction a b is b a for a and b not zero. 6. We can only add and subtract fractions with a common denominator. 7. If the given fractions do not have the same denominator, convert each fraction to an equivalent fraction with the LCD as its denominator. GRAPHING CALCULATOR SKILLS Practice operations with fractions by hand before relying on the calculator to perform the work for you. At this point, use the calculator only as a check of your work. The calculator will display all answers as decimals. To convert an answer to a fraction, use the MATH menu. 1. Simplify 12 18 . 1 2 4 1 8 ENTER 1 ENTER MATH 2. 1 4 · 12 15 1 4 4 3 1 2 4 1 5 ENTER 1 ENTER MATH
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