To evaluate the expression [tex]\(-\frac{2}{3} \times 5 \frac{1}{6}\)[/tex], let's go through the correct steps:
### Step 1: Convert Mixed Number to Improper Fraction
First, we need to convert the mixed number [tex]\(5 \frac{1}{6}\)[/tex] into an improper fraction.
A mixed number [tex]\(a \frac{b}{c}\)[/tex] can be converted to an improper fraction as:
[tex]\[
a \frac{b}{c} = \frac{ac + b}{c}
\][/tex]
For [tex]\(5 \frac{1}{6}\)[/tex]:
[tex]\[
5 \frac{1}{6} = \frac{(5 \times 6) + 1}{6} = \frac{30 + 1}{6} = \frac{31}{6}
\][/tex]
### Step 2: Multiply the Fractions
Now we need to multiply [tex]\(-\frac{2}{3}\)[/tex] by [tex]\(\frac{31}{6}\)[/tex]:
[tex]\[
-\frac{2}{3} \times \frac{31}{6}
\][/tex]
Multiply the numerators and the denominators:
[tex]\[
-\frac{2 \times 31}{3 \times 6} = -\frac{62}{18}
\][/tex]
### Step 3: Simplify the Fraction
To simplify [tex]\(-\frac{62}{18}\)[/tex], we find the greatest common divisor (GCD) of 62 and 18. The GCD is 2.
Divide the numerator and the denominator by 2:
[tex]\[
-\frac{62 \div 2}{18 \div 2} = -\frac{31}{9}
\][/tex]
### Step 4: Convert to Mixed Number (if required)
In this case, we are left with [tex]\(-\frac{31}{9}\)[/tex] which is the improper fraction form. Since we want a final simplified form, we note that:
[tex]\[
-\frac{31}{9} \approx -3.444
\][/tex]
Given the context, the primary steps are complete, and the calculation simplifies:
Finally, the value is:
\2
Thus, Calvin made an error in his problem-solving approach. Specifically, he incorrectly broke up [tex]\(5 \frac{1}{6}\)[/tex] instead of converting it correctly into an improper fraction before proceeding with the multiplication.
