Question

How many hours are in \[2\dfrac{1}{2}\] days?

Answer 1

Hint: In this question, we find the hours from split mixed fraction (which unit is days). To convert split mixed fraction into improper fraction, first we write spit mixed fraction into sum of a whole number and a fraction. Then write the whole number as an equivalent fraction. After that we added two fractions by using fraction adding rule. Then we multiply the one-day hours with the result, which will be obtained by adding two fractions.

Complete step by step answer:
In this question, we find the hours from given data. The data is given in the form of split mixed fraction which is converting into improper fraction. First, we know about what is split mixed fraction and the improper fraction. Fraction number is defined as the form which has the value in numerator and the value in denominator.
Split mixed fraction: the fraction which has a whole number and a fraction. The whole number and a fraction are writing together.
And we know that the hours in a day are \[24\]. Then to find the hour from given data, we multiply the one-day hours into improper fractions.
Let’s take an example. a is the whole number and \[\dfrac{b}{c}\] is the fraction number then the split mixed fraction is written as \[a\dfrac{b}{c}\].
Improper fraction: the fraction which has the value in numerator is greater than the value in denominator is known as improper fraction.
Let’s take an example. a is the value of numerator and b is the value of denominator, and a is greater than b. then improper fraction is written as.
\[\dfrac{a}{b}\;\;\;\;\;\;\left( {where\;a > b} \right)\]
Now according to the question, the split mixed fraction \[2\dfrac{1}{2}\] is given, which is converted into an improper fraction.
First, we write the split mixed fraction into the sum of the whole number and a fraction.
Then, \[2\dfrac{1}{2}\] is written as below.
\[ \Rightarrow 2\dfrac{1}{2} = 2 + \dfrac{1}{2}\]
Then, we write the whole number in the form of a fraction number as below.
\[ \Rightarrow 2 = \dfrac{4}{2}\]
Now we will put it in the above operation as,
\[ \Rightarrow \dfrac{4}{2} + \dfrac{1}{2}\]
For adding two fractions, we add numerator to numerator. Denominators are common.
Then,
\[ \Rightarrow \dfrac{{4 + 1}}{2} = \dfrac{5}{2}\]
Hence, the split mixed fraction \[2\dfrac{1}{2}\] is written in the improper fraction as \[\dfrac{5}{2}\].
We know that, the hours in a day \[ = 24\]
Then, the hours in \[\dfrac{5}{2}\] days,
\[ \Rightarrow \dfrac{5}{2} \times 24\]
Then, we write the whole number in the form of a fraction number as below.
\[ \Rightarrow \dfrac{5}{2} \times \dfrac{{24}}{1}\]
For adding two fractions, we add numerator to numerator. Denominators are common.
Then,
\[ \Rightarrow \dfrac{{5 \times 24}}{{2 \times 1}}\]
\[ \Rightarrow \dfrac{{120}}{2}\]
Now, we divide the numerator with denominator as,
\[\therefore \dfrac{{120}}{2} = 60\]

Therefore, the number of hours in \[2\dfrac{1}{2}\]days are \[60\;{\text{hours}}\].

Note:
If you want to convert a split mixed fraction into improper fraction. First you want to convert the whole number into fraction numbers. Then add two fractions. If the denominator is the same for both fractions, then you add both numerators and take the denominator as common.