4.2 Multiply and divide fractions  (Page 5/7)

$\frac{7}{21}$

$\frac{8}{24}$

$\frac{15}{20}$

$\frac{12}{18}$

$-\frac{40}{88}$

$-\frac{63}{99}$

$-\frac{108}{63}$

$-\frac{104}{48}$

$\frac{120}{252}$

$\frac{182}{294}$

$-\frac{168}{192}$

$-\frac{140}{224}$

$\frac{11x}{11y}$

$\frac{15a}{15b}$

$-\frac{3x}{12y}$

$-\frac{4x}{32y}$

$\frac{14x^2}{21y}$

$\frac{24a}{32b^2}$

$\frac{1}{2}·\frac{2}{3}$

$\frac{1}{2}·\frac{5}{8}$

$\frac{1}{3}·\frac{5}{6}$

$\frac{1}{3}·\frac{2}{5}$

$\frac{2}{5}·\frac{1}{3}$

$\frac{1}{2}·\frac{3}{8}$

$\frac{3}{4}·\frac{9}{10}$

$\frac{4}{5}·\frac{2}{7}$

$-\frac{2}{3}\left(-\frac{3}{8}\right)$

$-\frac{3}{4}\left(-\frac{4}{9}\right)$

$-\frac{5}{9}·\frac{3}{10}$

$-\frac{3}{8}·\frac{4}{15}$

$\frac{7}{12}\left(-\frac{8}{21}\right)$

$\frac{5}{12}\left(-\frac{8}{15}\right)$

$\left(-\frac{14}{15}\right)\left(\frac{9}{20}\right)$

$\left(-\frac{9}{10}\right)\left(\frac{25}{33}\right)$

$\left(-\frac{63}{84}\right)\left(-\frac{44}{90}\right)$

$\left(-\frac{33}{60}\right)\left(-\frac{40}{88}\right)$

$4·\frac{5}{11}$

$5·\frac{8}{3}$

$\frac{3}{7}·21n$

$\frac{5}{6}·30m$

$\mathrm{-28}p\left(-\frac{1}{4}\right)$

$\mathrm{-51}q\left(-\frac{1}{3}\right)$

$\mathrm{-8}\left(\frac{17}{4}\right)$

$\frac{14}{5}\left(\mathrm{-15}\right)$

$\mathrm{-1}\left(-\frac{3}{8}\right)$

$\left(\mathrm{-1}\right)\left(-\frac{6}{7}\right)$

${\left(\frac{2}{3}\right)}^3$

${\left(\frac{4}{5}\right)}^2$

${\left(\frac{6}{5}\right)}^4$

${\left(\frac{4}{7}\right)}^4$

$\frac{3}{4}$

$\frac{2}{3}$

$-\frac{5}{17}$

$-\frac{6}{19}$

$\frac{11}{8}$

$\mathrm{-13}$

$\mathrm{-19}$

$\mathrm{-1}$

$1$

$\frac{1}{2}÷\frac{1}{4}$

$\frac{1}{2}÷\frac{1}{8}$

$2÷\frac{1}{5}$

$3÷\frac{1}{4}$

$\frac{1}{2}÷\frac{1}{4}$

$\frac{1}{2}÷\frac{1}{8}$

$\frac{3}{4}÷\frac{2}{3}$

$\frac{4}{5}÷\frac{3}{4}$

$-\frac{4}{5}÷\frac{4}{7}$

$-\frac{3}{4}÷\frac{3}{5}$

$-\frac{7}{9}÷\left(-\frac{7}{9}\right)$

$-\frac{5}{6}÷\left(-\frac{5}{6}\right)$

$\frac{3}{4}÷\frac{x}{11}$

$\frac{2}{5}÷\frac{y}{9}$

$\frac{5}{8}÷\frac{a}{10}$

$\frac{5}{6}÷\frac{c}{15}$

$\frac{5}{18}÷\left(-\frac{15}{24}\right)$

$\frac{7}{18}÷\left(-\frac{14}{27}\right)$

$\frac{7p}{12}÷\frac{21p}{8}$

$\frac{5q}{12}÷\frac{15q}{8}$

$\frac{8u}{15}÷\frac{12v}{25}$

$\frac{12r}{25}÷\frac{18s}{35}$

$\mathrm{-5}÷\frac{1}{2}$

$\mathrm{-3}÷\frac{1}{4}$

$\frac{3}{4}÷\left(\mathrm{-12}\right)$

$\frac{2}{5}÷\left(\mathrm{-10}\right)$

$\mathrm{-18}÷\left(-\frac{9}{2}\right)$

$\mathrm{-15}÷\left(-\frac{5}{3}\right)$

$\frac{1}{2}÷\left(-\frac{3}{4}\right)÷\frac{7}{8}$

$\frac{11}{2}÷\frac{7}{8}·\frac{2}{11}$

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. Write your result as an improper fraction and as a mixed number.

ⓑ Measuring cups usually come in sets of $\frac{1}{8},\frac{1}{4},\frac{1}{3},\frac{1}{2},\text{and}1$ cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the recipe.

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.

1. ⓐ How much condensed milk will Nina need? Show your calculation. Write your result as an improper fraction and as a mixed number.
2. ⓑ Measuring cups usually come in sets of $\frac{1}{8},\frac{1}{4},\frac{1}{3},\frac{1}{2},\text{and}1$ cup. Draw a diagram to show two different ways that Nina could measure the condensed milk she needs.

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?

Portions Kristen has $\frac{3}{4}$ yards of ribbon. She wants to cut it into equal parts to make hair ribbons for her daughter’s $6$ dolls. How long will each doll’s hair ribbon be?

Explain how you find the reciprocal of a fraction.

Explain how you find the reciprocal of a negative fraction.

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.

Give an example from everyday life that demonstrates how $\frac{1}{2}·\frac{2}{3}\text{is}\frac{1}{3}.$