Question

Jada evaluates the expression 2/3 + 3/4 Her work is shown Line 1 2/3+3/4=8/12+9/12 Line 2 =17/24 Part A Is the work shown in Line 1 correct if it is correct, explain why it is necessary to perform that step to add the fractions if it is incorrect, explain why it is incorrect and how to correct it

Answer 1

Jada's initial step in finding a common denominator was incorrect. The correct LCM of the denominators 3 and 4 is 12, leading to a sum of 17/12, not 17/24 as she calculated.

Step-by-step explanation:

The work shown in Line 1 by Jada is incorrect because she has attempted to find a common denominator without properly accounting for the least common multiple (LCM) of the original denominators.

The correct method for adding the fractions 2/3 and 3/4 is by first determining the LCM of 3 and 4, which is 12, and then converting each fraction to have the common denominator of 12, which will give us the fractions 8/12 and 9/12. Then we can add the numerators to get 17/12, which is the correct sum of the two fractions.

Jada's mistake was in her assertion that the sum of 8/12 and 9/12 equals 17/24. This is incorrect because, although 17 is the correct sum of the numerators, the denominator should remain 12.

To correct her mistake, she should keep the common denominator of 12 to get the correct answer: 17/12.