Question

If $\dfrac{k}{2} \times \dfrac{3}{7} = 2\dfrac{4}{5}$ of $1\dfrac{1}{4}$, what will be the value of $k$ ?
A) $13\dfrac{1}{3}$
B) $16\dfrac{1}{3}$
C) $11\dfrac{1}{3}$
D) $15\dfrac{1}{3}$

Answer 1

Hint: First of all, separate the terms of the left – hand side and right – hand side and solve them separately. In the right – hand side term, convert the mixed fraction into improper fraction and multiply both of them. Then, make the left – hand side term equal to right – hand side term and find the value of $k$.

Complete Step by Step Solution:
We have to find the value of $k$ in the equation, $\dfrac{k}{2} \times \dfrac{3}{7} = 2\dfrac{4}{5}$ of $1\dfrac{1}{4}$
Therefore, separate the terms on the left – hand side and right – hand side so, that we can solve this question easily.
So, taking the left – hand side terms –
$ \Rightarrow \dfrac{k}{2} \times \dfrac{3}{7}$
To multiply the two fractions, we multiply the numerator with the numerator of another fraction and denominator with the denominator of another fraction. Hence, multiplying the fractions in the left – hand side, we get –
$ \Rightarrow \dfrac{{3k}}{{14}}$
Now, taking the right – hand side term of the question, we get –
 $ \Rightarrow 2\dfrac{4}{5}$ of $1\dfrac{1}{4}$
We have to convert $2\dfrac{4}{5}$ and $1\dfrac{1}{4}$ into improper fraction as both of these fractions are in mixed fraction. To convert the mixed fraction into improper fraction we use the following steps to do it:
Step – 1: Multiply the denominator of the fractional part of mixed fraction with the whole number part of mixed fraction.
Step – 2: Find the sum of the numerator of the fractional part of the mixed fraction with the result of step 1.
Step – 3: Keep the denominator of the fraction same as when it was in the form of mixed fraction.
Step – 4: Put the result of step 2 in the place of numerator and will get the mixed fraction converted to improper fraction.
So, $2\dfrac{4}{5}$ can be converted into improper fraction as $\dfrac{{14}}{5}$ and $1\dfrac{1}{4}$ can be converted as $\dfrac{5}{4}$ . Now, we have to multiply both of these fractions
$
  \therefore \dfrac{{14}}{5} \times \dfrac{5}{4} \\
   \Rightarrow \dfrac{{14}}{4} \\
 $
This can be converted into the simplest form as $\dfrac{7}{2}$ .
Now, again writing the equation in the question, we get –
$ \Rightarrow \dfrac{{3k}}{{14}} = \dfrac{7}{2}$
Doing cross – multiplication, we get –
$
   \Rightarrow 3k = \dfrac{{14 \times 7}}{2} \\
   \Rightarrow 3k = 7 \times 7 \\
   \Rightarrow 3k = 49 \\
   \Rightarrow k = \dfrac{{49}}{3} \\
 $
Hence, the value of $k$ in $\dfrac{k}{2} \times \dfrac{3}{7} = 2\dfrac{4}{5}$ of $1\dfrac{1}{4}$ is $\dfrac{{49}}{3}$.
When $\dfrac{{49}}{3}$ is converted to mixed fraction, we get $16\dfrac{1}{3}$.

Hence, option (B) is the correct answer.

Note:
In these types of questions students can check their answers by putting the value of $k$, which they got in their answer, in the equation in the question and if the equation satisfies that condition, it means that their answer is true.