ADV. MATH 6: 003 (LMS)

MathXL for School: Practice & Problem Solving (LMS graded)

Part 1 of 4

Divide [tex]\(-3 \frac{1}{6} \div 11 \frac{2}{5}\)[/tex]. Explain each step you used to find the quotient.

What is the first step in finding this quotient? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a fraction. Use a comma to separate answers as needed.)

A. Multiply the whole parts of the mixed numbers. The product is [tex]\(\square\)[/tex].

B. Multiply the fraction parts of the mixed numbers. The product is [tex]\(\square\)[/tex].

C. Find the reciprocal of the dividend. The reciprocal is [tex]\(\square\)[/tex].

D. Convert the mixed numbers to fractions. The fractions are [tex]\(\square\)[/tex].

To divide the mixed numbers [tex]\(-3 \frac{1}{6}\)[/tex] and [tex]\(11 \frac{2}{5}\)[/tex], the first step is to convert these mixed numbers into improper fractions. Here's how you do it:

1. Convert [tex]\(-3 \frac{1}{6}\)[/tex] to an improper fraction:

The whole number part is [tex]\(-3\)[/tex], and the fraction part is [tex]\(\frac{1}{6}\)[/tex].

[tex]\[
\text{Improper Fraction} = -\left((3 \times 6) + 1\right) / 6 = -19/6
\][/tex]

2. Convert [tex]\(11 \frac{2}{5}\)[/tex] to an improper fraction:

The whole number part is [tex]\(11\)[/tex], and the fraction part is [tex]\(\frac{2}{5}\)[/tex].

[tex]\[
\text{Improper Fraction} = \left((11 \times 5) + 2\right) / 5 = 57/5
\][/tex]

Now, the mixed numbers have been converted to the fractions [tex]\(-19/6\)[/tex] and [tex]\(57/5\)[/tex]. So the correct choice is:

D. Convert the mixed numbers to fractions. The fractions are [tex]\(-19/6, 57/5\)[/tex].