Question

Esmerelda simplified a complex fraction. Her work is shown below.  What errors did Esmerelda make? Select three options. Esmerelda converted the mixed number to the wrong improper fraction. Esmerelda added the numerators. Esmerelda added the denominators. Esmerelda did not divide –24 by 6 correctly. Esmerelda did not use the reciprocal of the divisor. ​

Answer 1

Picture relating to the question is attached below :

Answer:

Esmerelda did not use the recipro al of the Divisor.

Esmerelda added the numerator

Esmerelda added the denominator

Explanation:

Esmerelda's work:

-5 1/4 ÷ 3/2= -21/4 ÷3/2 = (-21/4)(3/2) = -24/6 = - 4

Esmerelda's errors:

When changing the quotient sign to multiplication ; the reciprocal of the denominator should be used to divide the numerator :

Hence,

-21/4 ÷3/2 = (-21/4)(3/2) (wrong expression)

-21/4 ÷3/2 = (-21/4)(2/3) (correct expression)

Also,

(-21/4)(3/2) = -24/6 ( wrong simplification)

The bracket symbol indicates multiplication. Hence, the values should be multiplied. The two Numerator values and the two denominator values.

Answer 2

Answer:

• Esmerelda added the numerators.
• Esmerelda added the denominators.
• Esmerelda did not use the reciprocal of the divisor. ​

Explanation:

When multiplying fractions, you are not to add them up as Esmerelda did. Rather you are to multiply them. The same goes for denominators as well.

If you want to divide a fraction by another fraction, you are to use the reciprocal of the divisor to multiplier the fraction to be divided. In this instance therefore, Esmerelda should have multiplied -21/4 by 2/3 which is the reciprocal of 3/2.

The correct working should have been:

$= \frac{-\frac{21}{4} }{\frac{3}{2} } = (-\frac{21}{4}) (\frac{2}{3}) = -\frac{42}{12} = -3.5$