Question

problems 8–10: spiral review
determine each quotient.
$6 \div \frac{1}{3}$
$4 \div \frac{1}{9}$
$\frac{1}{10} \div 8$

Explanation:

For \( 6 \div \frac{1}{3} \)

Step1: Recall division of fractions rule (multiply by reciprocal)

To divide a number by a fraction, we multiply the number by the reciprocal of the fraction. The reciprocal of \(\frac{1}{3}\) is \(3\). So, \( 6 \div \frac{1}{3}=6\times3\)

Step2: Perform the multiplication

\(6\times3 = 18\)

Step1: Apply division of fractions rule

The reciprocal of \(\frac{1}{9}\) is \(9\). So, \(4\div\frac{1}{9}=4\times9\)

Step2: Calculate the product

\(4\times9 = 36\)

Step1: Use division of fractions rule (rewrite 8 as a fraction)

We can write \(8\) as \(\frac{8}{1}\). The reciprocal of \(\frac{8}{1}\) is \(\frac{1}{8}\). So, \(\frac{1}{10}\div8=\frac{1}{10}\times\frac{1}{8}\)

Step2: Multiply the fractions

When multiplying fractions, we multiply the numerators and the denominators. So, \(\frac{1\times1}{10\times8}=\frac{1}{80}\)

Answer:

\(18\)

For \( 4 \div \frac{1}{9} \)