Question

What is equivalent to $\dfrac{3}{4}$ when the denominator is 68?

Answer 1

Hint: Since we need to find the equivalent term to the fraction term so we can confirm ourselves that we will get a fraction only and of which we are already given the denominator as 68. So, we need to find such a fraction using the correct form.

Complete step-by-step solution:
How to find it?
Equivalent fractions are formed by multiplying the numerator and denominator of a fraction by the same number. This is the same as multiplying by 1. The value of the fraction does not change, only what it looks like. The ratio between the top and bottom stays the same.
Now clearly if we multiply the numerator and denominator of fraction by 2 and 7 respectively, we will get
$\dfrac{3}{4}\times \dfrac{2}{2}=\dfrac{6}{8}$ and for the second case we will get $\dfrac{3}{4}\times \dfrac{7}{7}=\dfrac{21}{28}$ .
Since what we did was the trial method as exactly, we don’t know what we will get. But if we move through the logic, we can think that the denominator of the equivalent term is 68 and the denominator of the original term is 4. So, in short, we need to find a number such that if we multiply it by 4, we will get 68 only then we would be able to find any fraction that would be equivalent to the given fraction after simplifications.
So now, $4\times 17=68$
therefore, we will get,
$\dfrac{3}{4}\times \dfrac{17}{17}=\dfrac{51}{68}$
And hence the above fraction is the equivalent fraction to $\dfrac{3}{4}$ .

Note: There is no such chances of error in this question if you solve it with full attention and know its procedure. Because the possible points of mistakes are calculation mistakes while calculating the term when 68 was divided 4 or while multiplying 3 with 17. So be careful while doing that.