The simplified expression of [tex]5\frac{1}{6} -7\frac{1}{3}[/tex] is[tex]-2\frac{1}{6}[/tex] .
A fraction represented with its quotient and remainder is called a mixed fraction.
To convert a mixed number into an improper fraction, multiply the whole number with the denominator of the proper fraction. Add the numerator of the proper fraction to this product to obtain the numerator of the improper fraction.
According to the given question
We have an expression
[tex]5\frac{1}{6} -7\frac{1}{3}[/tex]
Before, simplifying the expression convert the given mixed fraction into improper fraction of the given expression.
So, [tex]5\frac{1}{6} =\frac{31}{6}[/tex]
and, [tex]7\frac{1}{3} =\frac{22}{3}[/tex]
Substitute these values in the given expression
⇒ [tex]5\frac{1}{6} -7\frac{1}{3} = \frac{31}{6} -\frac{22}{3}[/tex]
⇒[tex]5\frac{1}{6} -7\frac{1}{3} = \frac{31-2(22)}{6}[/tex]
⇒[tex]5\frac{1}{6} -7\frac{1}{3} =\frac{31-44}{6}[/tex]
⇒[tex]5\frac{1}{6} -7\frac{1}{3} =\frac{-13}{6}[/tex]
⇒[tex]5\frac{1}{6} -7\frac{1}{3} = -2\frac{1}{6}[/tex]
Hence, the simplified expression of [tex]5\frac{1}{6} -7\frac{1}{3}[/tex] is[tex]-2\frac{1}{6}[/tex] .
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