Question

How do you write \[ - 2\dfrac{5}{6}\] as an improper fraction?

Answer 1

Hint: We will multiply \[2\] with \[6\], and then add it with \[5\] to get the final improper fraction. On doing some simplification we get the required answer.

Complete Step by Step Solution:
The given mixed fraction is: \[ - 2\dfrac{5}{6}\].
So, if we omit the negative sign, the fraction has a whole number \[2\] along with the proper fraction \[\dfrac{5}{6}\]
So, firstly we will multiply \[2\] and \[6\] to get the value of the fraction with the whole number part.
So, the multiplication of \[6\] and \[2\] is \[ = 2 \times 6 = 12.\]
Now, as it is a mixed fraction, we have to add this value with the numerator part of the proper fraction.
By doing it, we get:
\[ \Rightarrow 12 + 5 = 17.\]
So, the numerator of the required improper fraction will be \[ = 17.\]
Now, the denominator will remain the same as \[6\].

Therefore, the required improper fraction will be \[ - \dfrac{{17}}{6}\].

Additional Information: Four types of fractions do exist.
They are:
\[(1)\]Unit fractions: Fractions with numerator \[1\] are called unit fractions.
Example: \[\dfrac{1}{2}\].
\[(2)\]Proper fractions: Fractions in which the numerator is less than the denominator are called proper fractions.
Example: \[\dfrac{2}{3}\].
\[(3)\]Improper fractions: Fractions in which the numerator is greater than or equal to the denominator are called improper fractions.
Example: \[\dfrac{4}{3}\].
\[(4)\]Mixed fractions: Fractions consist of a whole number along with a proper fraction.
Example: \[3\dfrac{2}{3}\].
If a mixed fraction is given in the following way:\[a\dfrac{b}{c}\].
Then we can convert it into an improper fraction by using the following method: \[\dfrac{{a \times c + b}}{c}\].

Note: Numerator part of the fraction states how much part it contains over the denominator part of the fraction.
Only mixed fractions can be converted into the improper fraction.
Alternative way to solution:
The given fraction is \[ - 2\dfrac{5}{6}\].
Now, we can write it as following way:
\[ \Rightarrow - \left( {2 + \dfrac{5}{6}} \right)\].
By doing multiplication, we get:
\[ \Rightarrow - \left( {\dfrac{{2 \times 6}}{6} + \dfrac{5}{6}} \right)\].
Now, by doing further simplification:
\[ \Rightarrow - \left( {\dfrac{{12}}{6} + \dfrac{5}{6}} \right)\].
Now, by solving it, we get:
\[ \Rightarrow - \left( {\dfrac{{12 + 5}}{6}} \right)\].
So, the required improper fraction is \[ - \dfrac{{17}}{6}\].