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Chapter 5: Problem 69

Perform the indicated operations. If possible, reduce the answer to its lowest terms. \(6 \frac{3}{5} \div 1 \frac{1}{10}\)

Short Answer

Expert verified
The result of the operation is 6.

Step by step solution

01

Convert the mixed numbers to improper fractions

A mixed number can be converted to an improper fraction by multiplying the whole number with the denominator and adding the numerator. This result becomes the new numerator and the denominator remains the same. So \(6 \frac{3}{5}\) will be converted to \(\frac{6*5 + 3}{5}\) = \(\frac{33}{5}\). The fraction \(1 \frac{1}{10}\) will be converted to \(\frac{1*10 + 1}{10}\) = \(\frac{11}{10}\).
02

Switch to multiplication of fractions

Division of fractions is similar to multiplication, where we multiply the first fraction with the reciprocal of the second fraction. Thus, the problem \(6 \frac{3}{5} \div 1 \frac{1}{10}\) that we are now solving will become \(\frac{33}{5} * \frac{10}{11}\).
03

Multiply the fractions

Here, multiply the numerators together to get the new numerator, and multiply the denominators to get the new denominator. This yields \(\frac{33*10}{5*11} = \frac{330}{55}\).
04

Simplify the result

Finally, simplify the fraction to its reduced terms if possible. Here, as 330 and 55 have a common factor, the fraction can be reduced to \(\frac{330}{55} = \frac{6}{1}\) or 6.

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Most popular questions from this chapter

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,3, \frac{3}{2}, \frac{3}{4}, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3, \frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(2,6,10,14, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,7,-7, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{4}\), when \(a_{1}=9, r=-\frac{1}{3}\).
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