Question

Write a fraction equivalent to \[\dfrac{3}{4}\] with the numerator 15.

Answer 1

Hint: Here, we will be multiplying the numerator and denominator by the same number to get the equivalent fraction. Equivalent fractions are fractions which represent the same part of a group.

Complete step by step answer:
A fraction is a number which represents a part of a group. It is written as \[\dfrac{a}{b}\], where \[a\] is called the numerator and \[b\] is called the denominator.
Equivalent fractions are the fractions which represent equal parts of the group. We can obtain the equivalent fraction of a given fraction by either multiplying or dividing both the numerator and the denominator by the same number.
We need to identify the relation between the numerator of the given fraction and the numerator of the required equivalent fraction.
We can observe that \[3 \times 5 = 15\].
This means that multiplying the numerator 3 by 5 gives us the result 15.
Now, we will multiply both the numerator and the denominator of the fraction \[\dfrac{3}{4}\] by 5 to get the required equivalent fraction with numerator 15.
\[
  \dfrac{3}{4} = \dfrac{{3 \times 5}}{{4 \times 5}} \\
   = \dfrac{{15}}{{20}} \\
\]
Here, \[\dfrac{{15}}{{20}}\] is the required equivalent fraction with numerator 15.


Note:
We can also solve these types of problems in another way.
Let the denominator of the required equivalent fraction as \[x\] and equate the fraction and the equivalent fraction, that is \[\dfrac{3}{4} = \dfrac{{15}}{x}\].
Now, the product of the numerator of the given fraction 3 and the denominator of the equivalent fraction \[x\], will be equal to the product of the numerator of the equivalent fraction 15 and the denominator of the given fraction 4, that is \[3 \times x = 15 \times 4\]. We can multiply the terms to get \[3x = 60\].
By dividing both sides of this expression by 3, we get the denominator of the equivalent fraction \[x = 20\]. Thus, we get the required equivalent fraction \[\dfrac{{15}}{{20}}\].