Question

Smerelda 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


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

Explanation:

ACTUAL ANSWER

(-5¼)/(3/2)

= -{(20+1)/4}/(3/2) //CONVERTING INTO IMPROPER FRACTION

= (-21/4)/(3/2)

= (-21/4) x (2/3) // MULTIPLYING BY RECIPROCAL

 = (-21x2)/(4x3)

= -42/12

= -(7x6)/(2x6) TAKING 7 AS COMMON FACTOR

= -7/2

STEPS FOLLOWED BY ESMERELDA

(-5¼)/(3/2)

= -{(20+1)/4}/(3/2)

= -(21/4)/(3/2)

= -(21/4) x (3/2)

= -(21+3)/(4+2)

= - (24/6)

= -4

HENCE THE ERRORS COMMITTED BY HER ARE:-

1. ESMERALDA ADDED THE NUMERATORS

2. ESMERALDA ADDED THE DENOMINATORS

3. ESMERALDA DID NOT USE THE RECIPROCAL OF THE DIVISOE