Question

Express the ratios in the simplest form: 85: 561.

Answer 1

Hint: Ratios can also be written as fractions. Hence, write the given ratio as fractions and cancel the common factors to get the simplest form.

Complete step-by-step answer:
Ratio, in mathematics, indicates how many times one number is contained in the other number. It also shows the relative sizes of two or more values. Ratios can be expressed in different ways, for example, using “:” between the quantities is one way of expressing the ratio. Writing the numbers in the form of fractions is the other way of expressing the ratio between two numbers.
These are also the two most used forms of expressing the ratio between two numbers.
The simplest form of the ratio is when the numbers are expressed as natural numbers with no common factors between them. For example, 2: 4 can be written in the simplest form as 1: 2.

The ratio we are given is 85: 561, which we need to express in the simplest form.
We first convert it into fraction form.
\[85:561 = \dfrac{{85}}{{561}}\]
Next, we simplify the fraction by canceling the common factors. We know that the factors of 85 are 17 and 5.
The number 561 is a multiple of 17, then, we cancel the factor 17 to get the simplest form.
\[85:561 = \dfrac{5}{{33}}\]
We now convert the fraction back into ratio form.
\[85:561 = 5:33\]
Hence, the simplest form of 85: 561 is 5: 33.

Note: You can also directly cancel the common factors without converting it into a fractional form. It is just easy to visualize the factors in the fractional form.