1.5 Visualize Fractions

Find three fractions equivalent to $\frac{3}{5} .$

Find three fractions equivalent to $\frac{4}{5} .$

Simplify: $- \frac{42}{54} .$

Simplify: $- \frac{45}{81} .$

Simplify: $- \frac{69}{120} .$

Simplify: $- \frac{120}{192} .$

Simplify: $\frac{7 x}{7 y} .$

Simplify: $\frac{3 a}{3 b} .$

Multiply: $- \frac{11}{12} \cdot \frac{5}{7} .$

Multiply: $- \frac{10}{28} \cdot \frac{8}{15} .$

Multiply: $- \frac{9}{20} \cdot \frac{5}{12} .$

Multiply: $\frac{11}{3} \left(−9 a\right) .$

Multiply: $\frac{13}{7} \left(−14 b\right) .$

Divide: $- \frac{2}{3} \div \frac{n}{5} .$

Divide: $- \frac{3}{5} \div \frac{p}{7} .$

Divide: $- \frac{5}{8} \div \frac{q}{3} .$

Find the quotient: $- \frac{7}{27} \div \left(- \frac{35}{36}\right) .$

Find the quotient: $- \frac{5}{14} \div \left(- \frac{15}{28}\right) .$

Simplify: $\frac{\frac{2}{3}}{\frac{5}{6}} .$

Simplify: $\frac{\frac{3}{7}}{\frac{6}{11}} .$

Simplify: $\frac{\frac{a}{8}}{\frac{a b}{6}} .$

Simplify: $\frac{\frac{p}{2}}{\frac{p q}{8}} .$

Simplify: $\frac{4 - 2 \left(3\right)}{2^{2} + 2} .$

Simplify: $\frac{6 - 3 \left(5\right)}{3^{2} + 3} .$

Simplify: $\frac{4 - 4 \left(6\right)}{3^{2} + 3} .$

Simplify: $\frac{4 \left(−3\right) + 6 \left(−2\right)}{−3 \left(2\right) - 2} .$

Simplify: $\frac{8 \left(−2\right) + 4 \left(−3\right)}{−5 \left(2\right) + 3} .$

Simplify: $\frac{7 \left(−1\right) + 9 \left(−3\right)}{−5 \left(3\right) - 2} .$

Translate the English phrase into an algebraic expression: the quotient of the difference of m and n, and p.

Translate the English phrase into an algebraic expression: the quotient of the difference of a and b, and cd.

Translate the English phrase into an algebraic expression: the quotient of the sum of $p$ and $q ,$ and $r$

Find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{3}{8}$

Find three fractions equivalent to the given fraction. Show your work, using figures or algebra.

$\frac{5}{9}$

Simplify.

$- \frac{40}{88}$

Simplify.

$- \frac{108}{63}$

Simplify.

$\frac{120}{252}$

Simplify.

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

Simplify.

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

Multiply.

$\frac{3}{4} \cdot \frac{9}{10}$

Multiply.

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

Multiply.

$- \frac{5}{9} \cdot \frac{3}{10}$

Multiply.

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

Multiply.

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

Multiply.

$4 \cdot \frac{5}{11}$

Multiply.

$\frac{3}{7} \cdot 21 n$

Multiply.

$−8 \left(\frac{17}{4}\right)$

Divide.

$\frac{3}{4} \div \frac{2}{3}$

Divide.

$- \frac{7}{9} \div \left(- \frac{7}{4}\right)$

Divide.

$\frac{3}{4} \div \frac{x}{11}$

Divide.

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

Divide.

$\frac{8 u}{15} \div \frac{12 v}{25}$

Divide.

$−5 \div \frac{1}{2}$

Divide.

$\frac{3}{4} \div \left(−12\right)$

Simplify.

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

Simplify.

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

Simplify.

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

Simplify.

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

Simplify.

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

Simplify.

$\frac{−6 + 6}{8 + 4}$

Simplify.

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

Simplify.

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

Simplify.

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

Simplify.

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

Simplify.

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

Simplify.

$\frac{7 \cdot 4 - 2 \left(8 - 5\right)}{9 \cdot 3 - 3 \cdot 5}$

Simplify.

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

Translate each English phrase into an algebraic expression.

the quotient of r and the sum of s and 10

Translate each English phrase into an algebraic expression.

the quotient of the difference of $x \text{and} y , \text{and} - 3$

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 $\frac{1}{4} , \frac{1}{3} , \frac{1}{2} , \text{and} 1$ cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the cookie recipe.

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?

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.

Explain how you find the reciprocal of a fraction.