Question

divide.
$1\frac{1}{3}\div\frac{5}{6}=$
submit

Explanation:

Step1: Convert mixed number to improper fraction

To convert \(1\frac{1}{3}\) to an improper fraction, we multiply the whole number (1) by the denominator (3) and add the numerator (1). So, \(1\times3 + 1 = 4\), and the improper fraction is \(\frac{4}{3}\).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \(\frac{5}{6}\) is \(\frac{6}{5}\). So we have \(\frac{4}{3} \div \frac{5}{6} = \frac{4}{3} \times \frac{6}{5}\).

Step3: Multiply the fractions

Multiply the numerators: \(4\times6 = 24\). Multiply the denominators: \(3\times5 = 15\). So we get \(\frac{24}{15}\).

Step4: Simplify the fraction

We can simplify \(\frac{24}{15}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, \(\frac{24\div3}{15\div3} = \frac{8}{5}\), or as a mixed number, \(1\frac{3}{5}\). But in improper fraction form, it's \(\frac{8}{5}\) or as a decimal 1.6. However, the simplified fraction is \(\frac{8}{5}\) or \(1\frac{3}{5}\). But let's check the multiplication again. Wait, \(\frac{4}{3} \times \frac{6}{5}\): the 6 and 3 can be simplified before multiplying. 6 divided by 3 is 2, so we have \(\frac{4}{1} \times \frac{2}{5} = \frac{8}{5}\). Yep, that's correct.

Answer:

\(\frac{8}{5}\) (or \(1\frac{3}{5}\))