1.2E: Exercises

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Practice Makes Perfect

Simplify Fractions

Simplify the following:

\(−\dfrac{108}{63}\)
\(\dfrac{120}{252}\)
\(\dfrac{14}{21}\)
\(−\dfrac{210}{110}\)

Answer

\(−\dfrac{12}{7}\)
\(\dfrac{10}{21}\)
\(\dfrac{2}{3}\)
\(−\dfrac{21}{11}\)

Multiply and Divide Fractions

Perform the operation:

\(−\dfrac{3}{4}\left(−\dfrac{4}{9}\right)\)
\(\left(−\dfrac{14}{15}\right)\left(\dfrac{9}{20}\right)\)
\(\left(−\dfrac{63}{84}\right)\left(−\dfrac{44}{90}\right)\)
\(\dfrac{3}{7}⋅21\)
\(\dfrac{3}{4}÷\dfrac{1}{11}\)
\(\dfrac{5}{18}÷\left(−\dfrac{15}{24}\right)\)
\(\dfrac{8}{15}÷\dfrac{12}{25}\)
\(\dfrac{3}{4}÷(−12)\)
\(−\dfrac{\dfrac{8}{21} }{\dfrac{12}{35}}\)
\(−\dfrac{\dfrac{4}{5}}{2}\)
\(\dfrac{\dfrac{1}{3}}{\dfrac{1}{2}}\)

Answer

\(\dfrac{1}{3}\)
\(−\dfrac{21}{50}\)
\(\dfrac{11}{30}\)
\(9\)
\(\dfrac{33}{4}\)
\(−\dfrac{4}{9}\)
\(\dfrac{10}{9}\)
\(−\dfrac{1}{16}\)
\(−\dfrac{10}{9}\)
\(−\dfrac{2}{5}\)
\(\dfrac{2}{3}\)

Add and Subtract

\(\dfrac{7}{12}+\dfrac{5}{8}\)
\(\dfrac{7}{12}−\dfrac{9}{16}\)
\(−\dfrac{13}{30}+\dfrac{25}{42}\)
\(−\dfrac{39}{56}−\dfrac{22}{35}\)
\(−\dfrac{2}{3}−\left(−\dfrac{3}{4}\right)\)
\(\dfrac{1}{3}+\dfrac{1}{4}\)
\(\dfrac{2}{3}+\dfrac{1}{6}\)

Answer

\(\dfrac{29}{24}\)
\(\dfrac{1}{48}\)
\(\dfrac{17}{105}\)
\(−\dfrac{53}{40}\)
\(\dfrac{1}{12}\)
\(\dfrac{7}{12}\)
\(\dfrac{5}{6}\)

Order of Operations

Simplify

\(\dfrac{5⋅6−3⋅4}{4⋅5−2⋅3}\)
\(\dfrac{5^2−3^2}{3−5}\)
\(\dfrac{7⋅4−2(8−5)}{9⋅3−3⋅5}\)
\(\dfrac{9(8−2)−3(15−7)}{6(7−1)−3(17−9)}\)
\(\dfrac{2}{\dfrac{1}{3}+\dfrac{1}{5}}\)

Answer

\(\dfrac{9}{7}\)
\(−8\)
\(\dfrac{11}{6}\)
\(\dfrac{5}{2}\)
\(\dfrac{15}{4}\)

Writing Exercises

Why do you need a common denominator to add or subtract fractions? Explain.
How do you find the LCD of 2 fractions?
Explain how you find the reciprocal of a fraction.
Explain how you find the reciprocal of a negative number.

Answer: Answers will vary.