Question

What is \[1\dfrac{1}{4}\] divided by \[1\dfrac{2}{5}\]?

Answer 1

Hint: Here we have a division of two mixed fractions. A fraction is a part of the whole number it consists of two parts numerator and a denominator. First we need to convert the given mixed fraction into an improper fraction then we need to divide the obtained fractions to get the desired results.

Complete step-by-step answer:
Given \[1\dfrac{1}{4}\] and \[1\dfrac{2}{5}\].
That is \[1\dfrac{1}{4} = 1 + \dfrac{1}{4}\]
\[1\dfrac{1}{4} = \dfrac{{4 + 1}}{4}\]
\[ \Rightarrow 1\dfrac{1}{4} = \dfrac{5}{4}\]
Again \[1\dfrac{2}{5} = 1 + \dfrac{2}{5}\]
\[1\dfrac{2}{5} = \dfrac{{5 + 2}}{5}\]
\[ \Rightarrow 1\dfrac{2}{5} = \dfrac{7}{5}\]
Now we need to divide \[\dfrac{5}{4}\] and \[\dfrac{7}{5}\].
That is \[\dfrac{5}{4} \div \dfrac{7}{5}\]
Now reciprocate the second fraction by interchanging its numerator with the denominator. Multiply the second fraction with the first one by multiplying the numerator and denominator with each other.
\[ \Rightarrow \dfrac{5}{4} \times \dfrac{5}{7}\]
\[ \Rightarrow \dfrac{{5 \times 5}}{{4 \times 7}}\]
\[ \Rightarrow \dfrac{{25}}{{28}}\]. This is the exact form.
\[ \Rightarrow 0.893\]. This is the decimal form.
So, the correct answer is “0.893”.

Note: We have different types of fractions.
Proper fraction: A fraction in which the numerator is less than the denominator is known as a proper fraction. Example \[\dfrac{1}{4}\]. Improper fraction: A fraction where the numerator is greater than the denominator then it is known as an improper fraction. Example \[\dfrac{5}{4}\]. Mixed fraction: A mixed fraction refers to the combination of the natural number and the fraction. Example \[1\dfrac{1}{4}\]