Ratios Exercises

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}$$