1.4E: Exercises
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Practice Makes Perfect
Find Equivalent Fractions
In the following exercises, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
\dfrac{3}{8}
- Answer
-
\dfrac{6}{16}, \dfrac{9}{24}, \dfrac{12}{32}, answers may vary
\dfrac{5}{8}
\dfrac{5}{9}
- Answer
-
\dfrac{10}{18}, \dfrac{15}{27}, \dfrac{20}{36}, answers may vary
\dfrac{1}{8}
Simplify Fractions
In the following exercises, simplify.
-\dfrac{40}{88}
- Answer
-
-\dfrac{5}{11}
-\dfrac{63}{99}
-\dfrac{108}{63}
- Answer
-
-\dfrac{12}{7}
-\dfrac{104}{48}
\dfrac{120}{252}
- Answer
-
\dfrac{10}{21}
\dfrac{182}{294}
-\dfrac{3x}{12y}
- Answer
-
-\dfrac{x}{4y}
-\dfrac{4x}{32y}
\dfrac{14x^{2}}{21y}
- Answer
-
\dfrac{2x^{2}}{3y}
\dfrac{24a}{32b^{2}}
Multiply Fractions
In the following exercises, multiply.
\dfrac{3}{4}\cdot \dfrac{9}{10}
- Answer
-
\dfrac{27}{40}
\dfrac{4}{5}\cdot \dfrac{2}{7}
-\dfrac{2}{3}\cdot -\dfrac{3}{8}
- Answer
-
\dfrac{1}{4}
-\dfrac{3}{4}\left(-\dfrac{4}{9}\right)
-\dfrac{5}{9}\cdot \dfrac{3}{10}
- Answer
-
-\dfrac{1}{6}
-\dfrac{3}{8}\cdot \dfrac{4}{15}
\left(-\dfrac{14}{15}\right)\left(\dfrac{9}{20}\right)
- Answer
-
-\dfrac{21}{50}
\left(-\dfrac{9}{10}\right)\left(\dfrac{25}{33}\right)
\left(-\dfrac{63}{84}\right)\left(-\dfrac{44}{90}\right)
- Answer
-
\dfrac{11}{30}
\left(-\dfrac{63}{60}\right)\left(-\dfrac{40}{88}\right)
4\cdot \dfrac{5}{11}
- Answer
-
\dfrac{20}{11}
5\cdot \dfrac{8}{3}
\dfrac{3}{7}\cdot 21n
- Answer
-
9n
\dfrac{5}{6}\cdot 30m
-8\cdot\dfrac{17}{4}
- Answer
-
−34
(-1)\left(-\dfrac{6}{7}\right)
Divide Fractions
In the following exercises, divide.
\dfrac{3}{4}\div \dfrac{2}{3}
- Answer
-
\dfrac{9}{8}
\dfrac{4}{5}\div \dfrac{3}{4}
-\dfrac{7}{9}\div \left(-\dfrac{7}{4}\right)
- Answer
-
\dfrac{4}{9}
-\dfrac{5}{6}\div \left(-\dfrac{5}{6}\right)
\dfrac{3}{4}\div \dfrac{x}{11}
- Answer
-
\dfrac{33}{4x}
\dfrac{2}{5}\div \dfrac{y}{9}
\dfrac{5}{18}\div -\dfrac{15}{24}
- Answer
-
-\dfrac{4}{9}
\dfrac{7}{18}\div \left(-\dfrac{14}{27}\right)
\dfrac{8u}{15} \div \dfrac{12v}{25}
- Answer
-
\dfrac{10u}{9v}
\dfrac{12r}{25}\div \dfrac{18s}{35}
-5\div \dfrac{1}{2}
- Answer
-
-10
-3\div \dfrac{1}{4}
\dfrac{3}{4}\div (-12)
- Answer
-
\dfrac{1}{16}
-15\div -\dfrac{5}{3}
In the following exercises, simplify.
\dfrac{-\dfrac{8}{21}}{\dfrac{12}{35}}
- Answer
-
-\dfrac{10}{9}
\dfrac{-\dfrac{9}{16}}{\dfrac{33}{40}}
\dfrac{-\dfrac{4}{5}}{2}
- Answer
-
-\dfrac{2}{5}
\dfrac{5}{\dfrac{3}{10}}
\dfrac{\dfrac{m}{3}}{\dfrac{n}{2}}
- Answer
-
\dfrac{2m}{3n}
\dfrac{-\dfrac{3}{8}}{-\dfrac{y}{12}}
Simplify Expressions Written with a Fraction Bar
In the following exercises, simplify.
\dfrac{22 + 3}{10}
- Answer
-
\dfrac{5}{2}
\dfrac{19 - 4}{6}
\dfrac{48}{24 - 15}
- Answer
-
\dfrac{16}{3}
\dfrac{46}{4 + 4}
\dfrac{-6 + 6}{8 + 4}
- Answer
-
0
\dfrac{-6 + 3}{17 - 8}
\dfrac{4\cdot 3}{6\cdot 6}
- Answer
-
\dfrac{1}{3}
\dfrac{6\cdot 6}{9\cdot 2}
\dfrac{4^{2} - 1}{25}
- Answer
-
\dfrac{3}{5}
\dfrac{7^{2} + 1}{60}
\dfrac{8\cdot 3 + 2\cdot 9}{14 + 3}
- Answer
-
\dfrac{42}{17}
\dfrac{9\cdot 6 - 4\cdot 7}{22 + 3}
\dfrac{5\cdot 6 - 3\cdot 4}{4\cdot 5 -2\cdot 3}
- Answer
-
\dfrac{9}{7}
\dfrac{8\cdot 9 - 7\cdot 6}{5\cdot 6 - 9\cdot 2}
\dfrac{5^{2} - 3^{2}}{3 - 5}
- Answer
-
-8
\dfrac{6^{2} - 4^{2}}{4 - 6}
\dfrac{7\cdot 4 - 2(8 - 5)}{9\cdot 3 - 3\cdot 5}
- Answer
-
\dfrac{11}{6}
\dfrac{9\cdot 7 - 3(12- 8)}{8\cdot 7- 6\cdot 6}
\dfrac{9(8-2)-3(15-7)}{6(7-1) - 3(17-9)}
- Answer
-
\dfrac{5}{2}
\dfrac{8(9-2) - 4(14 - 9)}{7(8-3)-3(16 -9)}
Translate Phrases to Expressions with Fractions
In the following exercises, translate each English phrase into an algebraic expression.
the quotient of r and the sum of s and 10
- Answer
-
\dfrac{r}{s + 10}
the quotient of A and the difference of 3 and B
the quotient of the difference of x and y, and −3
- Answer
-
\dfrac{x - y}{-3}
the quotient of the sum of m and n, and 4q
Everyday Math
Baking. A recipe for chocolate chip cookies calls for \frac{3}{4} cup brown sugar. Imelda wants to double the recipe.
- How much brown sugar will Imelda need? Show your calculation.
- Measuring cups usually come in sets of \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, and 1 cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the cookie recipe.
- Answer
-
- 1\frac{1}{2} cups
- answers will vary
Baking. Nina is making 4 pans of fudge to serve after a music recital. For each pan, she needs \frac{2}{3} cup of condensed milk.
- How much condensed milk will Nina need? Show your calculation.
- Measuring cups usually come in sets of \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, and 1 cup. Draw a diagram to show two different ways that Nina could measure the condensed milk needed for 4 pans of fudge.
Portions Don purchased a bulk package of candy that weighs 5 pounds. He wants to sell the candy in little bags that hold \frac{1}{4} pound. How many little bags of candy can he fill from the bulk package?
- Answer
-
20 bags
Portions Kristen has \frac{3}{4} yards of ribbon that she wants to cut into 6 equal parts to make hair ribbons for her daughter’s 6 dolls. How long will each doll’s hair ribbon be?
Writing Exercises
Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into 6 or 8 slices. Would he prefer 3 out of 6 slices or 4 out of 8 slices? Rafael replied that since he wasn’t very hungry, he would prefer 3 out of 6 slices. Explain what is wrong with Rafael’s reasoning.
- Answer
-
Answers may vary
Give an example from everyday life that demonstrates how \dfrac{1}{2}\cdot \dfrac{2}{3} is \dfrac{1}{3}.
Explain how you find the reciprocal of a fraction.
- Answer
-
Answers may vary
Explain how you find the reciprocal of a negative number.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ After looking at the checklist, do you think you are well prepared for the next section? Why or why not?
