5.8: Exercise Supplement
- Page ID
- 52598
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Addition and Subtractions of Fractions with Like and Unlike Denominators, and Addition and Subtraction of Mixed Numbers ([link], [link], [link])
For problems 1-53, perform each indicated operation and write the result in simplest form.
Exercise \(\PageIndex{1}\)
\(\dfrac{3}{4} + \dfrac{5}{8}\)
- Answer
-
\(\dfrac{11}{8}\) or \(1 \dfrac{3}{8}\)
Exercise \(\PageIndex{2}\)
\(\dfrac{9}{16} + \dfrac{1}{4}\)
Exercise \(\PageIndex{3}\)
\(\dfrac{1}{8} + \dfrac{3}{8}\)
- Answer
-
\(\dfrac{1}{2}\)
Exercise \(\PageIndex{4}\)
\(\dfrac{5}{7} + \dfrac{1}{14} + \dfrac{5}{21}\)
Exercise \(\PageIndex{5}\)
\(\dfrac{5}{6} + \dfrac{1}{3} + \dfrac{5}{21}\)
- Answer
-
\(\dfrac{59}{42} = 1 \dfrac{17}{42}\)
Exercise \(\PageIndex{6}\)
\(\dfrac{2}{5} + \dfrac{1}{8}\)
Exercise \(\PageIndex{7}\)
\(\dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{4}\)
- Answer
-
\(\dfrac{5}{8}\)
Exercise \(\PageIndex{8}\)
\(\dfrac{1}{16} + \dfrac{1}{10}\)
Exercise \(\PageIndex{9}\)
\(\dfrac{2}{7} + \dfrac{1}{3}\)
- Answer
-
\(\dfrac{13}{21}\)
Exercise \(\PageIndex{10}\)
\(2 \dfrac{1}{3} + \dfrac{1}{6}\)
Exercise \(\PageIndex{11}\)
\(3 \dfrac{11}{16} + \dfrac{3}{4}\)
- Answer
-
\(4 \dfrac{7}{16}\)
Exercise \(\PageIndex{12}\)
\(5 \dfrac{1}{12} + 3 \dfrac{1}{8}\)
Exercise \(\PageIndex{13}\)
\(16 \dfrac{2}{5} + 8 \dfrac{1}{4}\)
- Answer
-
\(8 \dfrac{3}{20}\)
Exercise \(\PageIndex{14}\)
\(1 \dfrac{1}{7} + 2 \dfrac{4}{7}\)
Exercise \(\PageIndex{15}\)
\(1 \dfrac{3}{8} + 0\)
- Answer
-
\(1 \dfrac{3}{8}\)
Exercise \(\PageIndex{16}\)
\(3 \dfrac{1}{10} + 4\)
Exercise \(\PageIndex{17}\)
\(18 \dfrac{2}{3} + 6\)
- Answer
-
\(24 \dfrac{2}{3}\)
Exercise \(\PageIndex{18}\)
\(1 \dfrac{4}{3} + 5 \dfrac{5}{4}\)
Exercise \(\PageIndex{19}\)
\(\dfrac{21}{4} + \dfrac{2}{3}\)
- Answer
-
\(\dfrac{71}{12} = 5 \dfrac{11}{12}\)
Exercise \(\PageIndex{20}\)
\(\dfrac{15}{16} - \dfrac{1}{8}\)
Exercise \(\PageIndex{21}\)
\(\dfrac{9}{11} - \dfrac{5}{22}\)
- Answer
-
\(\dfrac{13}{22}\)
Exercise \(\PageIndex{22}\)
\(6 \dfrac{2}{15} - 1 \dfrac{3}{10}\)
Exercise \(\PageIndex{23}\)
\(5 \dfrac{2}{3} + 8 \dfrac{1}{5} - 2 \dfrac{1}{4}\)
- Answer
-
\(11 \dfrac{37}{60}\)
Exercise \(\PageIndex{24}\)
\(8 \dfrac{3}{10} - 4 \dfrac{5}{6} - 3 \dfrac{1}{15}\)
Exercise \(\PageIndex{25}\)
\(\dfrac{11}{12} + \dfrac{1}{9} - \dfrac{1}{16}\)
- Answer
-
\(\dfrac{139}{144}\)
Exercise \(\PageIndex{26}\)
\(7 \dfrac{2}{9} - 5 \dfrac{5}{6} - 1 \dfrac{1}{3}\)
Exercise \(\PageIndex{27}\)
\(16 \dfrac{2}{5} - 8 \dfrac{1}{6} - 3 \dfrac{2}{15}\)
- Answer
-
\(5 \dfrac{1}{10}\)
Exercise \(\PageIndex{28}\)
\(4 \dfrac{1}{8} + 0 - \dfrac{32}{8}\)
Exercise \(\PageIndex{29}\)
\(4 \dfrac{1}{8} + 0 - \dfrac{32}{8}\)
- Answer
-
\(\dfrac{1}{8}\)
Exercise \(\PageIndex{30}\)
\(8 - 2 \dfrac{1}{3}\)
Exercise \(\PageIndex{31}\)
\(4 - 3 \dfrac{5}{16}\)
- Answer
-
\(\dfrac{11}{16}\)
Exercise \(\PageIndex{32}\)
\(6 \dfrac{3}{7} + 4\)
Exercise \(\PageIndex{33}\)
\(11 \dfrac{2}{11} - 3\)
- Answer
-
\(8 \dfrac{2}{11}\)
Exercise \(\PageIndex{34}\)
\(21 \dfrac{5}{8} - \dfrac{5}{8})
Exercise \(\PageIndex{35}\)
\(\dfrac{3}{4} + \dfrac{5}{16} \cdot \dfrac{4}{5}\)
- Answer
-
1
Exercise \(\PageIndex{36}\)
\(\dfrac{11}{12} + \dfrac{15}{16} \div 2 \dfrac{1}{2}\)
Exercise \(\PageIndex{37}\)
\(1 \dfrac{3}{10} + 2 \dfrac{2}{3} \div \dfrac{4}{9}\)
- Answer
-
\(7 \dfrac{3}{10}\)
Exercise \(\PageIndex{38}\)
\(8 \dfrac{3}{5} - 1 \dfrac{1}{14} \cdot \dfrac{3}{7}\)
Exercise \(\PageIndex{39}\)
\(2 \dfrac{3}{8} \div 3 \dfrac{9}{16} - \dfrac{1}{9}\)
- Answer
-
\(\dfrac{5}{9}\)
Exercise \(\PageIndex{40}\)
\(15 \dfrac{2}{5} \div 50 - \dfrac{1}{10}\)
Complex Fractions and Combinations of Operations with Fractions ([link],[link])
Exercise \(\PageIndex{41}\)
\(\dfrac{\dfrac{9}{16}}{\dfrac{21}{32}}\)
- Answer
-
\(\dfrac{6}{7}\)
Exercise \(\PageIndex{42}\)
\(\dfrac{\dfrac{10}{21}}{\dfrac{11}{14}}\)
Exercise \(\PageIndex{43}\)
\(1 \dfrac{\dfrac{7}{9}}{1 \dfrac{5}{27}}\)
- Answer
-
\(\dfrac{3}{2}\) or \(1 \dfrac{1}{2}\)
Exercise \(\PageIndex{44}\)
\(\dfrac{\dfrac{15}{17}}{\dfrac{50}{51}}\)
Exercise \(\PageIndex{45}\)
\(\dfrac{1 \dfrac{9}{16}}{2 \dfrac{11}{12}}\)
- Answer
-
\(\dfrac{15}{28}\)
Exercise \(\PageIndex{46}\)
\(\dfrac{8 \dfrac{4}{15}}{3}\)
Exercise \(\PageIndex{47}\)
\(\dfrac{9 \dfrac{1}{18}}{6}\)
- Answer
-
\(\dfrac{163}{108}\) or \(1 \dfrac{55}{108}\)
Exercise \(\PageIndex{48}\)
\(\dfrac{3 \dfrac{1}{4} + 2 \dfrac{1}{8}}{5 \dfrac{1}{6}}\)
Exercise \(\PageIndex{49}\)
\(\dfrac{3 + 2 \dfrac{1}{2}}{\dfrac{1}{4} + \dfrac{5}{6}}\)
- Answer
-
\(\dfrac{66}{13}\) or \(5 \dfrac{1}{13}\)
Exercise \(\PageIndex{50}\)
\(\dfrac{4 + 1 \dfrac{7}{10}}{9 - 2 \dfrac{1}{5}}\)
Exercise \(\PageIndex{51}\)
\(1 \dfrac{\dfrac{2}{5}}{9 - \dfrac{2}{2}}\)
- Answer
-
\(\dfrac{7}{40}\)
Exercise \(\PageIndex{52}\)
\(\dfrac{1 \dfrac{2}{3} \cdot (\dfrac{1}{4} + \dfrac{1}{5})}{1 \dfrac{1}{2}}\)
Exercise \(\PageIndex{53}\)
\(\dfrac{\dfrac{10}{23} \cdot (\dfrac{5}{6} + 2)}{\dfrac{8}{9}}\)
- Answer
-
\(\dfrac{255}{184}\) or \(1 \dfrac{71}{184}\)
Comparing Fractions
For problems 54-65, place each collection in order from smallest to largest.
Exercise \(\PageIndex{54}\)
\(\dfrac{1}{8}, \dfrac{3}{16}\)
Exercise \(\PageIndex{55}\)
\(\dfrac{3}{32}, \dfrac{1}{8}\)
- Answer
-
\(\dfrac{3}{32}, \dfrac{1}{8}\)
Exercise \(\PageIndex{56}\)
\(\dfrac{5}{16}, \dfrac{3}{24}\)
Exercise \(\PageIndex{57}\)
\(\dfrac{3}{10}, \dfrac{5}{6}\)
- Answer
-
\(\dfrac{3}{10}, \dfrac{5}{6}\)
Exercise \(\PageIndex{58}\)
\(\dfrac{2}{9}, \dfrac{1}{3}, \dfrac{1}{6}\)
Exercise \(\PageIndex{59}\)
\(\dfrac{3}{8}, \dfrac{8}{3}, \dfrac{19}{6}\)
- Answer
-
\(\dfrac{3}{8}, \dfrac{8}{3}, \dfrac{19}{6}\)
Exercise \(\PageIndex{60}\)
\(\dfrac{3}{5}, \dfrac{2}{10}, \dfrac{7}{20}\)
Exercise \(\PageIndex{61}\)
\(\dfrac{4}{7}, \dfrac{5}{9}\)
- Answer
-
\(\dfrac{5}{9}, \dfrac{4}{7}\)
Exercise \(\PageIndex{62}\)
\(\dfrac{4}{5}, \dfrac{5}{7}\)
Exercise \(\PageIndex{63}\)
\(\dfrac{5}{12}, \dfrac{4}{9}, \dfrac{7}{15}\)
- Answer
-
\(\dfrac{5}{12}, \dfrac{4}{9}, \dfrac{7}{15}\)
Exercise \(\PageIndex{64}\)
\(\dfrac{7}{36}, \dfrac{1}{24}, \dfrac{5}{12}\)
Exercise \(\PageIndex{65}\)
\(\dfrac{5}{8}, \dfrac{13}{16}, \dfrac{3}{4}\)
- Answer
-
\(\dfrac{5}{8}, \dfrac{3}{4}, \dfrac{13}{16}\)