Question

How do you write \[ - 7\dfrac{5}{{12}}\] as a decimal?

Answer 1

Hint: In this question, we have to represent the given number as decimal.
First, we need to convert the mixed fraction into an improper fraction. After that, we will convert the improper fraction to a decimal number by dividing the numerator by the denominator. Then we will get the required solution.

Complete step by step solution:
We need to write \[ - 7\dfrac{5}{{12}}\] as a decimal. But first, we will convert it into an improper fraction.
Steps to convert mixed fraction to improper fraction:
Multiply the whole number part by the fraction’s denominator.
Add the product to the numerator.
Then, write the result as the numerator, and the denominator is the same as in the mixed fraction.
Following the steps, we can convert \[ - 7\dfrac{5}{{12}}\] as an improper fraction,
We get, \[ - 7\dfrac{5}{{12}} = - \dfrac{{\left( {7 \times 12} \right) + 5}}{{12}} = - \dfrac{{89}}{{12}}\] .
Steps to convert a fraction to a decimal:
In fractions, the numerator is the number above the line and the denominator is the number below.
The line in a fraction that separates the numerator and the denominator represents division.
To convert a fraction to a decimal, divide the numerator by the denominator.
Write the numerator as the dividend as the denominator as the divisor.
Find a multiple of divisor, smaller than or equal to the dividend. Write the number as the quotient and write the multiple below the dividend. Subtract both the numbers and the resultant will be your new dividend.
If the new dividend is smaller than the divisor, then put a decimal in the quotient and add a zero behind the new dividend. And solve it again by using the above mentioned steps.
Now we need to convert \[ - \dfrac{{89}}{{12}}\] to a decimal.
Following the steps, we can convert \[ - \dfrac{{89}}{{12}}\] into decimal, we get,
$\begin{array}{*{20}{c}}
  {{\text{ }}7.4} \\
  { - 12)\overline {{\text{ }}89} } \\
  {{\text{ }}84} \\
  {{\text{ }}\left( - \right)} \\
  {{\text{ }}\overline {{\text{ 50}}} } \\
  {{\text{ }}48} \\
  {{\text{ }}\left( - \right)} \\
  {{\text{ }}\overline {{\text{ }}2} } \\
  {}
\end{array}$
\[ - \dfrac{{89}}{{12}} = - 7.4\] [We will take it up to one decimal place only.]

Hence, \[ - 7\dfrac{5}{{12}}\] as a decimal can be written as, \[ - 7.4\] .

Note: Proper fraction:
A fraction where the numerator (the top number) is less than the denominator(the bottom number). For example, \[\dfrac{1}{4},\dfrac{3}{5}\] etc.
Improper fraction:
A fraction where the numerator (the top number) is greater than the denominator (the bottom number).
For example, \[\dfrac{7}{5},\dfrac{3}{2}\] etc.
Mixed fraction:
A whole number and a proper fraction combined into one “Mixed fraction”.
For example, \[5\dfrac{1}{2},7\dfrac{1}{5}\] etc.