4.14: Fractions (Exercises)
- Last updated
- Jul 2, 2019
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4.1 - Visualize Fractions
In the following exercises, name the fraction of each figure that is shaded.
In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.
In the following exercises, convert the improper fraction to a mixed number.
- 5815
- 6311
In the following exercises, convert the mixed number to an improper fraction.
- 1214
- 945
- Find three fractions equivalent to 25. Show your work, using figures or algebra.
- Find three fractions equivalent to −43. Show your work, using figures or algebra.
In the following exercises, locate the numbers on a number line.
- 58,43,334, 4
- 14,−14,113,−113,72,−72
In the following exercises, order each pair of numbers, using < or >.
- −1___−25
- −212___−3
4.2 - Multiply and Divide Fractions
In the following exercises, simplify.
- −6384
- −90120
- −14a14b
- −8x8y
In the following exercises, multiply.
- 25⋅813
- −13⋅127
- 29⋅(−4532)
- 6m ⋅411
- −14 (−32)
- 315⋅178
In the following exercises, find the reciprocal.
- 29
- 154
- 3
- −14
- Fill in the chart.
Opposite | Absolute Value | Reciprocal | |
---|---|---|---|
−513 | |||
310 | |||
94 | |||
-12 |
In the following exercises, divide.
- 23÷16
- (−3x5)÷(−2y3)
- 45÷ 3
- 8 ÷223
- 823÷1112
4.3 - Multiply and Divide Mixed Numbers and Complex Fractions
In the following exercises, perform the indicated operation.
- 315⋅178
- −5712⋅4411
- 8 ÷223
- 823÷1112
In the following exercises, translate the English phrase into an algebraic expression.
- the quotient of 8 and y
- the quotient of V and the difference of h and 6
In the following exercises, simplify the complex fraction.
- 5845
- 89−4
- n438
- −156−112
In the following exercises, simplify.
- 5+165
- 8⋅4−523⋅12
- 8⋅7+5(8−10)9⋅3−6⋅4
4.4 - Add and Subtract Fractions with Common Denominators
In the following exercises, add.
- 38+28
- 45+15
- 25+15
- 1532+932
- x10+710
In the following exercises, subtract.
- 811−611
- 1112−512
- 45−y5
- −3130−730
- 32−(32)
- 1115−515−(−215)
4.5 - Add and Subtract Fractions with Different Denominators
In the following exercises, find the least common denominator.
- 13 and 112
- 13 and 45
- 815 and 1120
- 34,16, and 510
In the following exercises, change to equivalent fractions using the given LCD.
- 13 and 15, LCD = 15
- 38 and 56, LCD = 24
- −916 and 512, LCD = 48
- 13,34 and 45, LCD = 60
In the following exercises, perform the indicated operations and simplify.
- 15+23
- 1112−23
- −910−34
- −1136−1120
- −2225+940
- y10−13
- 25+(−59)
- 411÷27d
- 25+(−3n8)(−29n)
- (23)2(58)2
- (1112+38)÷(56−110)
In the following exercises, evaluate.
- y − 45 when (a) y = −45 (b) y = 14
- 6mn2 when m = 34 and n = −13
4.6 - Add and Subtract Mixed Numbers
In the following exercises, perform the indicated operation.
- 413+913
- 625+735
- 5811+2411
- 358+378
- 91320−41120
- 2310−1910
- 21112−1712
- 8611−2911
4.7 - Solve Equations with Fractions
In the following exercises, determine whether the each number is a solution of the given equation.
- x − 12 = 16:
- x = 1
- x = 23
- x = − \dfrac{1}{3}
- y + \dfrac{3}{5} = \dfrac{5}{9}:
- y = \dfrac{1}{2}
- y = \dfrac{52}{45}
- y = − \dfrac{2}{45}
In the following exercises, solve the equation.
- n + \dfrac{9}{11} = \dfrac{4}{11}
- x − \dfrac{1}{6} = \dfrac{7}{6}
- h − \left(- \dfrac{7}{8}\right) = − \dfrac{2}{5}
- \dfrac{x}{5} = −10
- −z = 23
In the following exercises, translate and solve.
- The sum of two-thirds and n is − \dfrac{3}{5}.
- The difference of q and one-tenth is \dfrac{1}{2}.
- The quotient of p and −4 is −8.
- Three-eighths of y is 24.
PRACTICE TEST
Convert the improper fraction to a mixed number.
- \dfrac{19}{5}
Convert the mixed number to an improper fraction.
- 3 \dfrac{2}{7}
Locate the numbers on a number line.
- \dfrac{1}{2}, 1 \dfrac{2}{3}, −2 \dfrac{3}{4}, and \dfrac{9}{4}
In the following exercises, simplify.
- \dfrac{5}{20}
- \dfrac{18r}{27s}
- \dfrac{1}{3} \cdot \dfrac{3}{4}
- \dfrac{3}{5} \cdot 15
- −36u\left(− \dfrac{4}{9}\right)
- −5 \dfrac{7}{12} \cdot 4 \dfrac{4}{11}
- − \dfrac{5}{6} \div \dfrac{5}{12}
- \dfrac{7}{11} \div \left(− \dfrac{7}{11}\right)
- \dfrac{9a}{10} \div \dfrac{15a}{8}
- −6 \dfrac{2}{5} \div 4
- \left(−15 \dfrac{5}{6}\right) \div \left(−3 \dfrac{1}{6}\right)
- \dfrac{−6}{\dfrac{6}{11}}
- \dfrac{\dfrac{p}{2}}{\dfrac{q}{5}}
- \dfrac{− \dfrac{4}{15}}{−2 \dfrac{2}{3}}
- \dfrac{9^{2} − 4^{2}}{9 − 4}
- \dfrac{2}{d} + \dfrac{9}{d}
- − \dfrac{3}{13} + \left(− \dfrac{4}{13}\right)
- − \dfrac{22}{25} + \dfrac{9}{40}
- \dfrac{2}{5} + \left(− \dfrac{7}{5}\right)
- − \dfrac{3}{10} + \left(- \dfrac{5}{8}\right)
- − \dfrac{3}{4} \div \dfrac{x}{3}
- \dfrac{2^{3} − 2^{2}}{\left(\dfrac{3}{4}\right)^{2}}
- \dfrac{\dfrac{5}{14} + \dfrac{1}{8}}{\dfrac{9}{56}}
Evaluate.
- x + \dfrac{1}{3} when (a) x = \dfrac{2}{3} (b) x = − \dfrac{5}{6}
In the following exercises, solve the equation.
- y + \dfrac{3}{5} = \dfrac{7}{5}
- a − \dfrac{3}{10} = − \dfrac{9}{10}
- f + \left(− \dfrac{2}{3}\right) = \dfrac{5}{12}
- \dfrac{m}{−2} = −16
- − \dfrac{2}{3}c = 18
- Translate and solve: The quotient of p and −4 is −8. Solve for p.
Contributors and Attributions
Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."