Expressing Ratios In Their Simplest Form - Questions

Question 1

29372

Express \(3.5:1.5\) in the simplest form

Answer

\(7:3\)

Worked Solution

\begin{aligned}
3.5: 1.5 &=\frac{35}{5}: \frac{15}{5} \\
&=7: 3
\end{aligned}

Question 2

29373

Express \(\dfrac{4}{3}:\dfrac{5}{2}\) in the simplest form

Answer

\(8:15\)

Worked Solution

\begin{aligned}
\frac{4}{3}: \frac{5}{2} &=\frac{8}{6}: \frac{15}{6} \\
&=8: 15
\end{aligned}

Question 3

29374

Express 4 kg to 600 g in the simplest form

Answer

\(20:3\)

Worked Solution

\begin{aligned}
4 \mathrm{~kg} =&4 \times 1000 \mathrm{~g} \\
=&4000 \mathrm{~g} \\
4 \mathrm{~kg}: 600 \mathrm{~g} &=4000: 600 \\
&=40: 6 \\
&=20: 3
\end{aligned}

Question 4

29375

\(1:5=x:20\), \(\therefore x = \)?

Answer

\(x=4\)

Worked Solution

\begin{aligned}
1: 5&=x: 20 \\
x: 20&=1: 5 \\
\frac{x}{20}&=\frac{1}{5} \\
x&=\frac{20}{5} \\
\therefore x&=4
\end{aligned}

Question 5

29376

Express \(12~\text{mm}:4.8~\text{cm}:0.15~\text{m}\) in simplest form

Answer

\(2:8:25\)

Worked Solution

\(\quad \begin{aligned}
0.15 \mathrm{~m}=& 0.15 \times 1000 \mathrm{~mm} \\
=& 150 \mathrm{~mm} \\
4.9 \mathrm{~cm}=& 4.8 \times 10 \mathrm{~mm} \\
=& 48 \mathrm{~mm} \\
\end{aligned}\)
\(\begin{aligned}
\therefore .12 \mathrm{~mm}: 4.8 \mathrm{~cm}: 0.15 \mathrm{~m}=&\frac{12}{3}: \frac{48}{3}: \frac{150}{3} \\
=& \frac{4}{2}: \frac{16}{2}:\frac{50}{2} \\
=& 2: 8: 25
\end{aligned}\)