Question

4 feet : 2 yardsSimplify the following ratios

Answer 1

The simplified ratio is 2 : 3

Step-by-step explanation:
`\begin{gathered} \text{Given ratio:} \\ 4\text{ f}eet\text{ : 2 yards} \end{gathered}`

To simplify the ratios, we need them to be in the same units.

The above ratio has different units. We need to convert both units in same units

conversion from yards to foot:

1 yard = 3 feet

2 yards = 2 × 3 = 6 feet

The ratio becomes:

`\begin{gathered} 4\text{ f}eet\text{ : 2 yards = }4\text{ f}eet\text{ : 6 f}eet \\ \\ \text{Simplifying:} \\ 4\text{ f}eet\text{ : 6 f}eet\text{ = }\frac{4\text{ f}eet}{6\text{ fe}et} \\ 2\text{ is common to both numerator and denominator} \\ \frac{4\text{ f}eet}{6\text{ fe}et}\text{ = }\frac{2(2)\text{ f}eet}{2(3)\text{ fe}et} \end{gathered}`

The simplified ratio:

`\begin{gathered} 2\text{ cancels out as well as the units as they are the same:} \\ \frac{4\text{ feet}}{6\text{ fe}et}\text{ = }(2)/(3) \\ \\ (2)/(3)\text{ = 2 : 3} \\ \\ \text{Hence, the simplified ratio is 2 : 3} \end{gathered}`