Question
Maria is adding the fractions 3/4 + 2/5
. She completed the following steps:
Step 1: Find the least common denominator of 4 and 5; which is 20.
Step 2: Rewrite the fractions with a denominator of 20: 3/4 = 15/20
and 2/5 = 8/20
.
Step 3: Add the fractions: 15/20 + 8/20 = 23/40
.
Step 4: Simplify the fraction, if possible: 23/40
.
Maria thinks the final answer is 23/40
.
A. Determine if Maria's steps and answer are correct.
B. If she made an error, identify the step where the error occurred and explain the error. Then, explain how to correct it.
C. If she is correct, explain why her answer is accurate.
(5 points)
0 / 10000 Word Limit
Skip to navigation
page 4 of 4
. She completed the following steps:
Step 1: Find the least common denominator of 4 and 5; which is 20.
Step 2: Rewrite the fractions with a denominator of 20: 3/4 = 15/20
and 2/5 = 8/20
.
Step 3: Add the fractions: 15/20 + 8/20 = 23/40
.
Step 4: Simplify the fraction, if possible: 23/40
.
Maria thinks the final answer is 23/40
.
A. Determine if Maria's steps and answer are correct.
B. If she made an error, identify the step where the error occurred and explain the error. Then, explain how to correct it.
C. If she is correct, explain why her answer is accurate.
(5 points)
0 / 10000 Word Limit
Skip to navigation
page 4 of 4
Answers
GPT-4o mini
A. Maria's steps contain an error, and her final answer is incorrect.
B. The error occurred in Step 3 when she added the fractions. The correct addition should be as follows:
- She correctly rewritten the fractions as \( \frac{15}{20} \) and \( \frac{8}{20} \).
- However, she incorrectly stated that \( \frac{15}{20} + \frac{8}{20} = \frac{23}{40} \).
- Instead, the correct addition is:
\[
\frac{15}{20} + \frac{8}{20} = \frac{15 + 8}{20} = \frac{23}{20}.
\]
- Step 4 is also incorrect in context, as \( \frac{23}{20} \) is not in its simplest form, but it is also an improper fraction.
C. To correct this, the answer should be \( \frac{23}{20} \), which can be simplified or expressed as a mixed number:
- \( \frac{23}{20} = 1 \frac{3}{20} \), meaning there is 1 whole and \( \frac{3}{20} \) left over.
Thus, Maria should conclude that the correct answer is \( \frac{23}{20} \) or \( 1 \frac{3}{20} \).
B. The error occurred in Step 3 when she added the fractions. The correct addition should be as follows:
- She correctly rewritten the fractions as \( \frac{15}{20} \) and \( \frac{8}{20} \).
- However, she incorrectly stated that \( \frac{15}{20} + \frac{8}{20} = \frac{23}{40} \).
- Instead, the correct addition is:
\[
\frac{15}{20} + \frac{8}{20} = \frac{15 + 8}{20} = \frac{23}{20}.
\]
- Step 4 is also incorrect in context, as \( \frac{23}{20} \) is not in its simplest form, but it is also an improper fraction.
C. To correct this, the answer should be \( \frac{23}{20} \), which can be simplified or expressed as a mixed number:
- \( \frac{23}{20} = 1 \frac{3}{20} \), meaning there is 1 whole and \( \frac{3}{20} \) left over.
Thus, Maria should conclude that the correct answer is \( \frac{23}{20} \) or \( 1 \frac{3}{20} \).