Question

A sweet dish requires 300g sugar and 900g flour. What is the fraction of sugar in the sweet?

Answer 1

Hint: In this question in order to calculate the fraction we can use the concept that the fraction is the ratio of the number of parts of the material for which it is to be calculated divided by the total number of parts of the whole substance i.e. $fraction = \dfrac{{number{\text{ of parts of material}}}}{{tota\operatorname{l} {\text{ number of parts }}}}$ .

Complete step-by-step solution:
Given,
\[{\text{Amount of sugar in sweet dish}} = 300g\]
\[{\text{ Amount of flour in sweet dish}} = 900g\]
$\therefore {\text{ Total amount of material required}} = 300g + 900g$
$ \Rightarrow {\text{ Total amount of material required}} = 1200g$
$\therefore {\text{ Fraction of sugar in the sweet = }}\dfrac{{{\text{amount of sugar in dish}}}}{{{\text{total amount of dish}}}}$
$ \Rightarrow {\text{ Fraction of sugar in the sweet = }}\dfrac{{300}}{{1200}}$
On simplifying further,
${\text{Fraction of sugar in the sweet = }}\dfrac{1}{4}$
$\therefore $ The final answer is the fraction of sugar in the sweet dish is $\dfrac{1}{4}$.

Note: The basic idea in this question is to find the number of parts of the material for which the fraction is to be calculated and also the total number of the parts of the whole substance. If the amount given in the question are of different units then all must be changed into the same unit otherwise the answer may be wrong. If the final answer comes in fraction then it may be changed into decimal in rounded form. Always try to solve step by step. Calculations should be done carefully to avoid any mistake. As the denominator is always greater than the numerator in this type of questions but if inverse comes then one can always check the solution for its correctness. The general form of calculating the fraction is, $fraction = \dfrac{{{x_i}}}{{{x_1} + {x_2} + {x_3} + \cdot \cdot \cdot + {x_n}}}$ where ${x_i}$ is the amount of part for which fraction is to be calculated and ${x_1},{x_2},{x_3}, \cdot \cdot \cdot ,{x_n}$ are the different amounts of parts present in the whole material.