Given:
The complex fraction is
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}[/tex]
Esmerelda simplified a complex fraction and steps are given.
To find:
The mistake of Esmerelda.
Solution:
We have,
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}[/tex]
Convert the mixed fraction in improper fraction.
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=\dfrac{-\dfrac{5\times 4+1}{4}}{\dfrac{3}{2}}[/tex]
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=\dfrac{-\dfrac{20+1}{4}}{\dfrac{3}{2}}[/tex]
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=\dfrac{-\dfrac{21}{4}}{\dfrac{3}{2}}[/tex]
Use the reciprocal of the divisor.
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=-\dfrac{21}{4}\times \dfrac{2}{3}[/tex]
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=-\dfrac{21\times 2}{4\times 3}[/tex]
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=-\dfrac{42}{12}[/tex]
[tex]\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=-\dfrac{7}{2}[/tex]
Therefore, the correct value of given fraction is [tex]-\dfrac{7}{2}[/tex].
Three mistakes of Esmerelda are:
1. Esmerelda added the numerators.
2. Esmerelda added the denominators.
3. Esmerelda did not use the reciprocal of the divisor.
