Answer to Question #135790 in Algebra for Faith

Question

1. Express the following ratios in their simplest form:
1.1. 3 to 12.
1.2. 90 to 30.
1.3. 1/5 to 1.
1.4. 50ç:R3,50.
1.5. 6cm:30mm.
1.6. 1:5:1.
1.7.15min:4hr.
1.8. 5/3:4.

Answer 1

$\textit(1.1)\\ \begin{aligned} 3 \hspace{0.1cm} \textsf{to} \hspace{0.1cm} 12 &= \frac{3}{3} : \frac{12}{3}\\&= 1 : 4 \end{aligned}\\ \textit(1.2)\\ \begin{aligned} 90 \hspace{0.1cm} \textsf{to} \hspace{0.1cm} 30 &= \frac{90}{30} : \frac{30}{30}\\&= 3 : 1 \end{aligned}\\ \textit(1.3)\\ \begin{aligned} \frac{1}{5} \hspace{0.1cm} \textsf{to} \hspace{0.1cm} 1 &= \frac{1}{5} \times 5: 1 \times 5 \\&= 1 : 5 \end{aligned}\\ \textit(1.4)\\ \begin{aligned} 50c \hspace{0.1cm} \textsf{to} \hspace{0.1cm} R 3.50&= \frac{50}{50} : \frac{350}{50}\\&= 1 : 7 \end{aligned}\\ \textit(1.5)\\ \begin{aligned} 6 \hspace{0.05cm}\textsf{cm} \hspace{0.1cm} \textsf{to} \hspace{0.1cm} 30\hspace{0.05cm}\textsf{mm}&= 60 \hspace{0.05cm}\textsf{mm}: 30 \hspace{0.05cm}\textsf{mm}\\&=\frac{60}{30} : \frac{30}{30} \\&=2 : 1 \end{aligned}\\ \textit(1.6)\\ 1:5:1 = 1:5:1\\ \textit(1.7)\\ \begin{aligned} 15 \hspace{0.05cm}\textsf{min} \hspace{0.1cm} \textsf{to} \hspace{0.1cm} 4\hspace{0.05cm}\textsf{hr}&= 15 \hspace{0.05cm}\textsf{min}: 4 \times 60 \hspace{0.05cm}\textsf{min}\\&= 15 : 240\\&=\frac{15}{15} : \frac{240}{15} \\&=1: 16 \end{aligned}\\ \textit(1.8)\\ \begin{aligned} \frac{5}{3}: 4 &=\frac{5}{3} \times 3: 4 \times 3\\&= 5 : 12 \end{aligned}$