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Savannah subtracted two fractions as follows. Examine her work.

[tex]\[
3 \frac{4}{5} - 2 \frac{1}{3}
\][/tex]

Step 1: [tex]\[ 3 \frac{4 \cdot 3}{5 \cdot 3} - 2 \frac{1 \cdot 5}{3 \cdot 5} \][/tex]

Step 2: [tex]\[ 3 \frac{12}{15} - 2 \frac{5}{15} \][/tex]

Step 3: [tex]\[ 3 - 2 = 1 \][/tex]

Step 4: [tex]\[ \frac{12}{15} - \frac{5}{15} = \frac{7}{15} \][/tex]

Step 5: [tex]\[ 3 \frac{12}{15} - 2 \frac{5}{15} = 1 \frac{7}{15} \][/tex]

What mistake, if any, did she make?

A. In Step 2, she chose the wrong common denominator.
B. She didn't make a mistake. All of her work is correct.
C. In Step 1, she multiplied by the wrong numbers.
D. In Step 4, she subtracted incorrectly.



Answer :

GinnyAnswer
Let's examine Savannah's subtraction of two mixed fractions step-by-step to determine if any mistakes were made.

Savannah is subtracting:
[tex]\[ 3 \frac{4}{5} - 2 \frac{1}{3} \][/tex]

Step 1:
[tex]\[ 3 \frac{4 \cdot 3}{5 \cdot 3} - 2 \frac{1 \cdot 5}{3 \cdot 5} \][/tex]
Savannah multiplies each fraction to convert the fractions to a common denominator:
[tex]\[ 3 \frac{4 \cdot 3}{5 \cdot 3} = 3 \frac{12}{15} \quad \text{and} \quad 2 \frac{1 \cdot 5}{3 \cdot 5} = 2 \frac{5}{15} \][/tex]

This step is correct.

Step 2:
[tex]\[ 3 \frac{12}{15} - 2 \frac{5}{15} \][/tex]
She successfully rewrites both fractions with the common denominator of 15:
[tex]\[ 3 \frac{12}{15} - 2 \frac{5}{15} \][/tex]

This step is also correct.

Step 3:
[tex]\[ 3 - 2 = 1 \][/tex]
She subtracts the whole numbers separately:
[tex]\[ 3 - 2 = 1 \][/tex]

This step is correct.

Step 4:
[tex]\[ \frac{12}{15} - \frac{5}{15} = \frac{7}{15} \][/tex]
She subtracts the fractions:
[tex]\[ \frac{12}{15} - \frac{5}{15} = \frac{7}{15} \][/tex]

This step is correct.

Step 5:
[tex]\[ 3 \frac{12}{15} - 2 \frac{5}{15} = 1 \frac{7}{15} \][/tex]
She combines the results of Step 3 and Step 4:
[tex]\[ 1 + \frac{7}{15} = 1 \frac{7}{15} \][/tex]

This step is correct.

So, analyzing all steps, we can conclude:
She didn't make a mistake. All of her work is correct.

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