Question

In a certain area, there are $35$ houses to $55$ businesses. How do you write the ratio of houses to businesses as a fraction in simplest form? Then explain its meaning too.

Answer 1

Hint: The given question is related to the concept of ratios and proportions. In order to understand the question, we should also understand the concept of ratios and proportions. Ratios are used to compare two things which share the same unit. It is represented by$\left( : \right)$or$\left( / \right)$. Proportions on the other hand, allows us to check the equality of the two ratios. It is represented by$\left( {::} \right)$or$\left( = \right)$.

Complete step-by-step solution:
Given is houses: businesses = $35:55$
The given ratio can also be rewritten in fractional form as $\dfrac{{35}}{{55}}$.
We can further simplify the fractional form by diving each of the numerator and denominator by number $5$ and we get,
$\Rightarrow \dfrac{7}{{11}}$
So, now the ratio of houses to businesses as a fraction is $\dfrac{7}{{11}}$.
The above found ratio of houses to businesses means that if you divide the businesses up into ($5$ groups of) $11$ and evenly assign the houses among these groups, then, each group would have $7$ houses.

Note: The given question was an easy application-based problem of ratios and proportions. Students should understand the signs for ratios and proportions separately. The most common mistake which students tend to make is use the sign of double colon in place of single colon. Double colon sign is used to indicate proportion while single colon is for ratios. The keyword to identify a ratio is that every ratio problem has the word ‘to’.