Add or subtract these 7ractions.-you answer in simplets form and as a mixed number where appropriate. a) \( 1 \frac{4}{5}+\frac{3}{4} \) e) \( 5 \frac{2}{9}-\frac{1}{3} \) F) \( 1 \frac{1}{4}+2 \frac{2}{5} \) g) \( 3 \frac{5}{6}-1 \frac{4}{5} \) h) \( 2 \frac{4}{7}-1 \frac{4}{5} \)
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To solve these problems, let’s break it down step by step, converting mixed numbers to improper fractions when necessary and finding a common denominator: a) \( 1 \frac{4}{5}+\frac{3}{4} \): Convert \( 1 \frac{4}{5} \) to an improper fraction: \( 1 \frac{4}{5} = \frac{9}{5} \) Find the common denominator between 5 and 4, which is 20: \( \frac{9}{5} = \frac{36}{20} \) and \( \frac{3}{4} = \frac{15}{20} \) Now add: \( \frac{36}{20} + \frac{15}{20} = \frac{51}{20} \) This is \( 2 \frac{11}{20} \). e) \( 5 \frac{2}{9}-\frac{1}{3} \): Convert \( 5 \frac{2}{9} = \frac{47}{9} \) and find the common denominator for 9 and 3, which is 9: \( \frac{1}{3} = \frac{3}{9} \) Now subtract: \( \frac{47}{9} - \frac{3}{9} = \frac{44}{9} \) This is \( 4 \frac{8}{9} \). f) \( 1 \frac{1}{4}+2 \frac{2}{5} \): Convert \( 1 \frac{1}{4} = \frac{5}{4} \) and \( 2 \frac{2}{5} = \frac{12}{5} \). The common denominator is 20: \( \frac{5}{4} = \frac{25}{20} \) and \( \frac{12}{5} = \frac{48}{20} \) Now add: \( \frac{25}{20} + \frac{48}{20} = \frac{73}{20} \) This is \( 3 \frac{13}{20} \). g) \( 3 \frac{5}{6}-1 \frac{4}{5} \): Convert \( 3 \frac{5}{6} = \frac{23}{6} \) and \( 1 \frac{4}{5} = \frac{9}{5} \). The common denominator is 30: \( \frac{23}{6} = \frac{115}{30} \) and \( \frac{9}{5} = \frac{54}{30} \) Now subtract: \( \frac{115}{30} - \frac{54}{30} = \frac{61}{30} \) This is \( 2 \frac{1}{30} \). h) \( 2 \frac{4}{7}-1 \frac{4}{5} \): Convert \( 2 \frac{4}{7} = \frac{18}{7} \) and \( 1 \frac{4}{5} = \frac{9}{5} \). The common denominator is 35: \( \frac{18}{7} = \frac{90}{35} \) and \( \frac{9}{5} = \frac{63}{35} \) Now subtract: \( \frac{90}{35} - \frac{63}{35} = \frac{27}{35} \) This is already in simplest form. Here are your answers: a) \( 2 \frac{11}{20} \) e) \( 4 \frac{8}{9} \) f) \( 3 \frac{13}{20} \) g) \( 2 \frac{1}{30} \) h) \( \frac{27}{35} \)