Question

Esmerelda simplified a complex fraction. Her work is shown below. Negative 5 and one-fourth divided by three-halves = negative StartFraction 21 over 4 EndFraction divided by three-halves = (Negative StartFraction 21 over 4 EndFraction) (Three-halves) = Negative StartFraction 24 over 6 EndFraction = negative 4

Answer 1

Given:

The complex fraction is

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}$

Esmerelda simplified a complex fraction and steps are given.

To find:

The mistake of Esmerelda.

Solution:

We have,

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}$

Convert the mixed fraction in improper fraction.

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=\dfrac{-\dfrac{5\times 4+1}{4}}{\dfrac{3}{2}}$

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=\dfrac{-\dfrac{20+1}{4}}{\dfrac{3}{2}}$

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=\dfrac{-\dfrac{21}{4}}{\dfrac{3}{2}}$

Use the reciprocal of the divisor.

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=-\dfrac{21}{4}\times \dfrac{2}{3}$

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=-\dfrac{21\times 2}{4\times 3}$

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=-\dfrac{42}{12}$

$\dfrac{-5\dfrac{1}{4}}{\dfrac{3}{2}}=-\dfrac{7}{2}$

Therefore, the correct value of given fraction is $-\dfrac{7}{2}$.

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.