Section 1.5. Fraction Multiplication and Division

Here is a table of multiplication factors that you may find useful. 12 1*12 2*6 3*4 24 1*24 2*12 3*8 4*6 34 1*34 2*17 46 1*46 2*23 58 1*58 2*29 70 1*70 2*35 5*14 7*10 82 1*82 2*41 14 1*14 2*7 25 1*25 5*5 35 1*35 5*7 48 1*48 2*24 3*16 4*12 6*8 60 1*60 2*30 3*20 4*15 5*12 6*10 72 1*72 2*36 4*18 8*9 100 1*100 2*50 4*25 5*20 10*10 15 1*15 3*5 26 1*26 2*13 36 1*36 2*18 3*12 4*9 6*6 50 1*50 2*25 5*10 62 1*62 2*31 74 1*74 2*37 121 1*121 11*11 16 1*16 2*8 4*4 27 1*27 3*9 38 1*38 2*19 52 1*52 2*26 4*13 63 1*63 3*21 7*9 75 1*75 3*25 5*15 144 1*144 2*72 3*48 4*36 18 1*18 2*9 3*6 28 1*28 2*14 4*7 40 1*40 2*20 4*10 5*8 54 1*54 2*27 3*18 6*9 64 1*64 2*32 4*16 8*8 76 1*76 2*38 4*19 169 1*169 13*13 20 1*20 2*10 4*5 30 1*30 2*15 3*10 5*6 42 1*42 2*21 3*14 6*7 55 1*55 5*11 65 1*65 5*13 77 1*77 7*11 225 1*225 15*15 3*75 5*45 9*25 21 1*21 3*7 32 1*32 2*16 4*8 44 1*44 2*22 4*11 56 1*56 2*28 4*14 7*8 66 1*66 2*33 3*22 6*11 78 1*78 2*39 3*26 6*13 22 1*22 2*11 33 1*33 3*11 45 1*45 3*15 5*9 57 1*57 3*19 68 1*68 2*34 4*17 80 1*80 2*40 4*20 5*16 8*10 6*24 8*18 9*16 12*12 Section 1.5: Fraction Multiplication and Division Chapter 1: Introduction to Algebra Equivalent Fraction Property: If the numerator and denominator of a fraction are multiplied (or divided) by the same nonzero number, then the resulting fraction is equivalent to the original fraction. • 2 2×4 8 For example: 3 = 3×4 = 12 (I multiplied the numerator and denominator by 4 to create an equivalent fraction. 2 8 We say the fractions 3 𝑎𝑛𝑑 12 are equivalent fractions. 5 9 Example: Rewrite the fraction as an equivalent fraction with 18 in the denominator. What do I need to multiply by? 5 9 2 2 × = 10 18 Answer: 10 18 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 = 18 9 =2 Steps to Simplify a fraction 1) Rewrite the numerator and denominator to show the common factors. You may factor the numerator and denominator into primes if needed. (or you can just divide the numerator and denominator by the same number if this seems easier) 2) Simplify using the equivalent fractions property by dividing out the common factor(s). 3) Multiply any remaining factors if you reduce using prime factors. Example of reducing a fraction. Recuced by rewriting numerator and denominator into primes and cancelling Example of reducing a fraction. Reduced by dividing the numerator and denominator by the same number. The reciprocal of a fraction is found by inverting the fraction, placing the numerator in the denominator and the denominator in the numerator. For example: The reciprocal of 3 𝑖𝑠 2 3 2 For example: The reciprocal of 4 𝑖𝑠 1 4 4 (𝑠𝑖𝑛𝑐𝑒 4 = 1) #17 – 28: Find the reciprocal. Leave your answer as an improper fraction when applicable. Do not reduce. 17) 19) 5 6 −3 7 18) 20) 3 4 −6 11 Section 1.5: Fraction Multiplication and Division Chapter 1: Introduction to Algebra Fraction Multiplication • • Multiply the numerators and multiply the denominators. 𝑎 𝑐 𝑎𝑐 If a, b, c and d are numbers where b ≠ 0, and d ≠ 0, 𝑏 × 𝑑 = 𝑏𝑑 For example: 3 5 4 3×4 12 × 7 = 5×7 = 35 #29 – 44: Multiply, write your answer in lowest terms. 29) 3 4 • 5 7 30) 2 3 • 4 9 Fraction Division • Multiply the first fraction by the reciprocal of the second. • If a, b, c and d are numbers where b ≠ 0, 𝑐 ≠ 0 and d ≠ 0 then: 𝑎 𝑏 𝑐 𝑎 𝑑 ÷𝑑 = 𝑏×𝑐 = For example: 2 3 5 2 𝑎𝑑 𝑏𝑐 7 14 ÷ 7 = 3 × 5 = 35 #45 – 60: Divide, write your answer in lowest terms. 45) 15 4 ÷ 5 12 46) 20 6 ÷ 4 9