Question

How do you write three equivalent ratios for $\dfrac{18}{6}$ ?

Answer 1

Hint: To find the equivalent rations for the given fraction $\dfrac{18}{6}$, we are going to multiply the numerator and the denominator by some numbers (say 2, 3, 4 and so on). But we only need three equivalent ratios so take any three numbers from the set which we have just written and then multiply the numerator and denominator of the given fraction to that number.

Complete step by step solution:
The fraction given in the above problem which we have to find three equivalent ratios is as follows:
$\dfrac{18}{6}$
Now, to write three equivalent ratios for this number meaning when we simplify those three ratios we will get the same value which we got by simplifying the above ratio. So, we are going to multiply 2 in the numerator and the denominator of the above problem and we get,
$=\dfrac{18\times 2}{6\times 2}$
Multiplying numerator and denominator by 2 we get,
$=\dfrac{36}{12}$
Let us mark the above ratio as the ratio A.
Now, we are going to multiply 3 in the numerator and the denominator of the given fraction and we get,
$=\dfrac{18\times 3}{6\times 3}$
The result of multiplication in the numerator and the denominator is equal to:
$=\dfrac{54}{18}$
Let us name the above ratio as ratio B.
Now, multiplying 4 in the numerator and denominator of the given fraction we get,
$=\dfrac{18\times 4}{6\times 4}$
The result of multiplication in the numerator and the denominator is equal to:
$=\dfrac{72}{24}$
Let us name the above ratio as ratio C.
Hence, we have found the three equivalent ratios for the given fraction as:
$=\dfrac{36}{12},\dfrac{54}{18},\dfrac{72}{24}$

Note: Now, to check whether the ratios we have found are correct or not is by simplifying these three ratios and see whether the simplification is same as that of the simplification of the given fraction.
The simplification of the given fraction is:
$\Rightarrow \dfrac{18}{6}=3$
Checking the simplification of three ratios we get,
$\begin{align}
  & \Rightarrow \dfrac{36}{12}=3, \\
 & \dfrac{54}{18}=3, \\
 & \dfrac{72}{24}=3 \\
\end{align}$
As you can see we are getting the same simplification value of the three ratios and are also as same as that of the given fraction.