Question
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Write \[\dfrac{{ - 14}}{{42}}\]in a form so that the numerator is equal to: \[42\].

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Hint:By reading the above question, we can understand that we have to find an equivalent fraction for \[\dfrac{{ - 14}}{{42}}\] where numerator is \[42\]. So, first convert the given fraction into the simplest form and multiply the desired number in the numerator as well as in the denominator to get the required equivalent fraction.

Complete step-by-step answer:
Given fraction = \[\dfrac{{ - 14}}{{42}}\]
Now try to convert the given fraction into the simplest form.
\[ \Rightarrow \dfrac{{ - 14}}{{42}} = \dfrac{{ - 7}}{{21}} = \dfrac{{ - 1}}{3}\]
Now to get the desired number in the numerator, multiply the desired number in the numerator as well as in the denominator.
As the given desired number in the numerator is \[42\], multiply the numerator and denominator with \[42\].
\[ \Rightarrow \dfrac{{ - 1 \times 42}}{{3 \times 42}}{\text{ = }}\dfrac{{ - 42}}{{126}}\]
\[\therefore \dfrac{{ - 42}}{{126}}\] is the equivalent fraction with the numerator \[42\].
All the fractions that we have got in the above problem are equivalent fractions.

Additional Information:Equivalent fractions: Fractions that may look different but have the same value, those fractions are called equivalent fractions. To get the equivalent fractions, you have to multiply the numerator and denominator with the same whole number except zero. Then we can get the equivalent fractions. We can get the first equivalent fraction in the series by converting into the simplest form.

Note:The only mistake anyone may do in this process is cancellation. Do not get confused about the sign. Any sign given in the numerator or denominator is the sign of the fraction. It is not denoted as the sign of the numerator or denominator. You have to multiply with the same number in the numerator and denominator. Because by multiplying with the same number, the value of the fraction does not change.