Ratios Exercises

1. Write the following ratios as reduced fractions.

a) $10$ to $24$

b) $\dfrac{5}{3}$ to $\dfrac{7}{6}$

c) $0.4$ to $1.8$

d) $1.6$ to $3.2$

e) $\dfrac{3}{5}$ to $0.6$

f) $0.5$ to $0.45$

Source: Algebra2Go, https://www.saddleback.edu/faculty/Lperez/Algebra2Go/prealgebra/ratios/ratiosHW.pdf
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Ratios - No Calculators!!

1. Write the following ratios as reduced fractions.

a) $10$ to $24$

$\begin{gathered} \dfrac{10}{24} \\ \\ \dfrac{10 / 2}{24 / 2} \\ \\ \dfrac{5}{12} \end{gathered}$

b) $\dfrac{5}{3}$ to $\dfrac{7}{6}$

$\begin{aligned} \dfrac{\dfrac{5}{3}}{\dfrac{7}{6}} &=\dfrac{5}{3} \div \dfrac{7}{6} \\ &=\dfrac{5}{\not{3}_{1}} \cdot \dfrac{\not{6}^{2}}{7} \\ &=\dfrac{10}{7} \end{aligned}$

c) $0.4$ to $1.8$

$\begin{aligned} &\dfrac{0.4}{1.8} \qquad LCD=10 \\ \\ &\dfrac{10(0.4)}{10(1.8)} \\ \\ &\dfrac{4}{18}=\dfrac{2}{9} \end{aligned}$

d) $1.6$ to $3.2$

$\begin{aligned} &\dfrac{1.6}{3.2} \\ \\ &\dfrac{10(1.6)}{10(3.2)} \\ \\&\dfrac{16}{32}=\dfrac{1}{2} \end{aligned}$

e) $\dfrac{3}{5}$ to $0.6$

$\begin{align} \begin{aligned} &\dfrac{\dfrac{3}{5}}{0 \cdot 6} \qquad \qquad LCD=10 \\ \\ &\dfrac{10 \, (\dfrac{3}{5})}{10 \, (0.6)} \\ \\  &\dfrac{6}{6}=1 \end{aligned} \end{align}$

f) $0.5$ to $0.45$

$\begin{align} \begin{gathered} \dfrac{0.5}{0.45} \qquad \qquad LCD=100 \\ \\ \dfrac{100(0.5)}{100(0.45)} \\ \\ \dfrac{50/5}{45 / 5} \\ \\ \dfrac{10}{9} \end{gathered} \end{align}$