Question

How do you convert \[ - 4\dfrac{1}{2}\] into a decimal and percent?

Answer 1

Hint: In this question, we will write a split mixed fraction into an improper fraction. To convert in improper fraction, first, we write a mixed fraction into the 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 the fraction adding a rule. Then, we convert a fraction form into a decimal number and after that calculate the percentage. To convert a fraction number into a decimal, the numerator is divided by the denominator of a fraction form. And for converting the percent form, the decimal number is multiplied with the number hundred.

Complete step by step solution:
In this question, the words improper fraction and split mixed fraction are used. First, we know about what is split mixed fraction and the improper fraction. We know about what fraction number. Fraction number is defined as the form which has the value in the numerator and the value in the denominator.
Split mixed fraction: the fraction which has a whole number and a fraction. The whole number and a fraction are writing together.
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 the numerator is greater than the value in the denominator is known as an 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 the improper fraction is written as.
\[\dfrac{a}{b}\;\;\;\;\;\;\left( {where\;a > b} \right)\].
Now come to the question, the split mixed fraction \[ - 4\dfrac{1}{2}\] 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, \[ - 4\dfrac{1}{2}\] is written as below.
\[ \Rightarrow - 4\dfrac{1}{2} = \left( { - 4} \right) + \dfrac{1}{2}\]
Then, we write the whole number in the form of a fraction number as below.
\[ \Rightarrow - 4 = - \dfrac{8}{2}\]
Put that into the above then,
\[ \Rightarrow \left( { - \dfrac{8}{2}} \right) + \dfrac{1}{2}\]
For adding two fractions, we add numerator to numerator. Denominators are common.
Then,
\[ \Rightarrow \dfrac{{ - 8 + 1}}{2} = - \dfrac{7}{2}\]
Then, split mixed fraction \[ - 4\dfrac{1}{2}\] is write in the improper fraction as \[ - \dfrac{7}{2}\]
Thus we convert fraction numbers into decimal form.
The fraction number is \[ = - \dfrac{7}{2}\]
In the fraction number, we divide the numerator with denominator to convert it into a decimal number,
Then, by calculating we have.
\[ = - 3.5\]
Therefore, the decimal form of \[ - 4\dfrac{1}{2}\] is \[ - 3.5\].
Now, the decimal number is converting into percent. For converting into percent from a decimal number, we multiply with the number hundred in the decimal number,
Then,
\[ = - 3.5 \times 100\]
Then we solve the above expression.
\[ = - 350\% \]

Therefore, the decimal and percent form of \[ - 4\dfrac{1}{2}\] is \[ - 3.5\] or \[ - 350\% \].

Note:
If you want to convert a split mixed fraction into an 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. After that, for converting a fraction number into a decimal number, you want to divide the numerator with the denominator.