4.3 Multiply and divide mixed numbers and complex fractions

$4\frac{3}{8}·\frac{7}{10}$

$2\frac{4}{9}·\frac{6}{7}$

$\frac{15}{22}·3\frac{3}{5}$

$\frac{25}{36}·6\frac{3}{10}$

$4\frac{2}{3}(\mathrm{-1}\frac{1}{8})$

$2\frac{2}{5}(\mathrm{-2}\frac{2}{9})$

$\mathrm{-4}\frac{4}{9}·5\frac{13}{16}$

$\mathrm{-1}\frac{7}{20}·2\frac{11}{12}$

$5\frac{1}{3}÷4$

$13\frac{1}{2}÷9$

$\mathrm{-12}÷3\frac{3}{11}$

$\mathrm{-7}÷5\frac{1}{4}$

$6\frac{3}{8}÷2\frac{1}{8}$

$2\frac{1}{5}÷1\frac{1}{10}$

$\mathrm{-9}\frac{3}{5}÷(\mathrm{-1}\frac{3}{5})$

$\mathrm{-18}\frac{3}{4}÷(\mathrm{-3}\frac{3}{4})$

the quotient of $5u$ and $11$

the quotient of $7v$ and $13$

the quotient of $p$ and $q$

the quotient of $a$ and $b$

$\frac{\frac{2}{3}}{\frac{8}{9}}$

$\frac{\frac{4}{5}}{\frac{8}{15}}$

$\frac{-\frac{8}{21}}{\frac{12}{35}}$

$\frac{-\frac{9}{16}}{\frac{33}{40}}$

$\frac{-\frac{4}{5}}{2}$

$\frac{-\frac{9}{10}}{3}$

$\frac{\frac{2}{5}}{8}$

$\frac{\frac{5}{3}}{10}$

$\frac{\frac{m}{3}}{\frac{n}{2}}$

$\frac{\frac{r}{5}}{\frac{s}{3}}$

$\frac{-\frac{x}{6}}{-\frac{8}{9}}$

$\frac{-\frac{3}{8}}{-\frac{y}{12}}$

$\frac{2\frac{4}{5}}{\frac{1}{10}}$

$\frac{4\frac{2}{3}}{\frac{1}{6}}$

$\frac{\frac{7}{9}}{\mathrm{-2}\frac{4}{5}}$

$\frac{\frac{3}{8}}{\mathrm{-6}\frac{3}{4}}$

$\frac{4+11}{8}$

$\frac{9+3}{7}$

$\frac{22+3}{10}$

$\frac{19-4}{6}$

$\frac{48}{24-15}$

$\frac{46}{4+4}$

$\frac{\mathrm{-6}+6}{8+4}$

$\frac{\mathrm{-6}+3}{17-8}$

$\frac{22-14}{19-13}$

$\frac{15+9}{18+12}$

$\frac{5\cdot 8}{\mathrm{-10}}$

$\frac{3\cdot 4}{\mathrm{-24}}$

$\frac{4\cdot 3}{6\cdot 6}$

$\frac{6\cdot 6}{9\cdot 2}$

$\frac{4^2-1}{25}$

$\frac{7^2+1}{60}$

$\frac{8\cdot 3+2\cdot 9}{14+3}$

$\frac{9\cdot 6-4\cdot 7}{22+3}$

$\frac{15\cdot 5-5^2}{2\cdot 10}$

$\frac{12\cdot 9-3^2}{3\cdot 18}$

$\frac{5\cdot 6-3\cdot 4}{4\cdot 5-2\cdot 3}$

$\frac{8\cdot 9-7\cdot 6}{5\cdot 6-9\cdot 2}$

$\frac{5^2-3^2}{3-5}$

$\frac{6^2-4^2}{4-6}$

$\frac{2+4(3)}{\mathrm{-3}-2^2}$

$\frac{7+3(5)}{\mathrm{-2}-3^2}$

$\frac{7\cdot 4-2(8-5)}{9.3-3.5}$

$\frac{9\cdot 7-3(12-8)}{8.7-6.6}$

$\frac{9(8-2)\mathrm{-3}(15-7)}{6(7-1)\mathrm{-3}(17-9)}$

$\frac{8(9-2)\mathrm{-4}(14-9)}{7(8-3)\mathrm{-3}(16-9)}$

Baking A recipe for chocolate chip cookies calls for $2\frac{1}{4}$ cups of flour. Graciela wants to double the recipe.

1. ⓐ How much flour will Graciela need? Show your calculation. Write your result as an improper fraction and as a mixed number.
2. ⓑ Measuring cups usually come in sets with cups for $\frac{1}{8},\frac{1}{4},\frac{1}{3},\frac{1}{2},\text{and}1$ cup. Draw a diagram to show two different ways that Graciela could measure out the flour needed to double the recipe.

Baking A booth at the county fair sells fudge by the pound. Their award winning “Chocolate Overdose” fudge contains $2\frac{2}{3}$ cups of chocolate chips per pound.

1. ⓐ How many cups of chocolate chips are in a half-pound of the fudge?
2. ⓑ The owners of the booth make the fudge in $10$ -pound batches. How many chocolate chips do they need to make a $10$ -pound batch? Write your results as improper fractions and as a mixed numbers.

Explain how to multiply mixed numbers.

Randy thinks that $3\frac{1}{2}·5\frac{1}{4}$ is $15\frac{1}{8}.$ Explain what is wrong with Randy’s thinking.

Explain why $-\frac{1}{2},\frac{\mathrm{-1}}{2},$ and $\frac{1}{\mathrm{-2}}$ are equivalent.