Question

A piece of string $25\dfrac{1}{2}$ inches long will be cut into $\dfrac{3}{4}$ inches pieces. How many pieces will there be?

Answer 1

Hint: In this question, we have to find the number of pieces from a string. Thus, we will use the fractional method and the basic mathematical rule to get the solution. First, we will change the mixed fraction into the simplest fraction form, that is we will multiply the denominator and the number and then add the numerator in the same to get the new numerator. After that, we will divide the new fractional term and $\dfrac{3}{4}$ because we have to find the number of pieces that will come after cutting the long piece of string. In the last, we will multiply the reciprocal of $\dfrac{3}{4}$ and do the necessary calculations, to get the solution.

Complete step-by-step answer:
According to the problem, we have to find the number of pieces from a string
Thus, we will use the fractional method and the basic mathematical rule to get the solution.
Let us first, change the mixed fraction into simplest fraction, which is we will multiply the denominator and the number and then add the numerator in the same to get the new numerator, we get
$\Rightarrow 25\dfrac{1}{2}\text{ inches}=\dfrac{25\times 2+1}{2}\text{ inches}=\dfrac{51}{2}\text{ inches}$ -------- (1)
Now, we know that the long string is cut into pieces of the length $\dfrac{3}{4}$ inches, thus, we will divide the value of equation (1) and $\dfrac{3}{4}$ inches to get the number of pieces, we get
$\Rightarrow \text{Number of pieces}=\dfrac{\dfrac{51}{2}}{\dfrac{3}{4}}$
So, we will take the reciprocal of the denominator, that is we will multiple $\dfrac{4}{3}$ in the above expression, we get
$\Rightarrow \text{Number of pieces}=\dfrac{51}{2}\times \dfrac{4}{3}$
In the end, we will make the necessary calculations, we get
$\Rightarrow \text{Number of pieces}=\dfrac{17}{1}\times \dfrac{2}{1}$
$\Rightarrow \text{Number of pieces}=34$
Therefore, if a piece of string $25\dfrac{1}{2}$ inches long will be cut into $\dfrac{3}{4}$ inches pieces, then there will be 34 pieces.

Note: While solving this problem, do the calculations properly to avoid mathematical error. Do not forget to mention the formula you are using to get the accurate answer. Do not forget to put the unit wherever applicable with the number.