Question

Is $ 3\dfrac{3}{4} $ bigger than $ 1\dfrac{{19}}{{21}}. $ How many times bigger?

Answer 1

Hint: First of all convert the given mixed fraction in the form of the simple fraction and then will take the ratio of one fraction with the other and then will simplify for the resultant required value.

Complete step by step solution:
Convert the given fraction $ 3\dfrac{3}{4} $ in the form of simple fraction.
Mixed number is the combination of a whole number and the fraction. Fraction is the number expressed in the form of the numerator and the denominator.
 $ 3\dfrac{3}{4} = \dfrac{{15}}{4} $ ….. (A)
Similarly take the given fraction and convert the given fraction in the form of the simple fraction.
 $ 1\dfrac{{19}}{{21}} = \dfrac{{40}}{{21}} $ ….. (B)
Take the ratio of equation (A) with the equation (B)
 $ \dfrac{{3\dfrac{3}{4}}}{{1\dfrac{{19}}{{21}}}} = \dfrac{{\dfrac{{15}}{4}}}{{\dfrac{{40}}{{21}}}} $
Simplify the above expression whose numerator’s denominator goes to the denominator and the denominator’s denominator goes to the numerator.
 $ \dfrac{{3\dfrac{3}{4}}}{{1\dfrac{{19}}{{21}}}} = \dfrac{{15 \times 21}}{{4 \times 40}} $
Find the factors of the term in the numerator and the denominator.
 $ \dfrac{{3\dfrac{3}{4}}}{{1\dfrac{{19}}{{21}}}} = \dfrac{{3 \times 5 \times 21}}{{4 \times 8 \times 5}} $
Common factors from the numerator and the denominator cancel each other. Remove from the numerator and the denominator.
 $ \dfrac{{3\dfrac{3}{4}}}{{1\dfrac{{19}}{{21}}}} = \dfrac{{3 \times 21}}{{4 \times 8}} $
Simplify the above expression-
 $ \dfrac{{3\dfrac{3}{4}}}{{1\dfrac{{19}}{{21}}}} = \dfrac{{63}}{{32}} $
Convert it in the form of mixed fraction-
 $ \dfrac{{3\dfrac{3}{4}}}{{1\dfrac{{19}}{{21}}}} = 1\dfrac{{31}}{{32}} $
The integer $ 3\dfrac{3}{4} $ is bigger $ 1\dfrac{{31}}{{32}} $ times than $ 1\dfrac{{19}}{{21}}. $

Note: Read the given word statements and understand it properly and then frame the equations accordingly and use division or multiplication for the required value. Always frame the mathematical expression properly since the solution depends on it only. Be good in finding the factors of the terms and remember multiples till twenty.
Fractions are the part of the whole. Generally, it represents any number of equal parts and it describes the part from a certain size and it is the number expressed in the form of numerator upon the denominator. Know the difference between the fraction and the percentage and apply accordingly.