Question

find the quotient.
$1\frac{1}{4} \div \frac{2}{3} = ?\frac{\\ }{\\ }$
give your answer as a mixed number in simplest form
enter the whole number.
start

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \(1\frac{1}{4}\) can be converted to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(1\frac{1}{4}\), we have \(a = 1\), \(b = 1\), \(c = 4\). Then \(\frac{1\times4 + 1}{4}=\frac{5}{4}\).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal. So \(\frac{5}{4}\div\frac{2}{3}=\frac{5}{4}\times\frac{3}{2}\).

Step3: Multiply the fractions

Multiply the numerators and denominators: \(\frac{5\times3}{4\times2}=\frac{15}{8}\).

Step4: Convert improper fraction to mixed number

To convert \(\frac{15}{8}\) to a mixed number, divide 15 by 8. \(15\div8 = 1\) with a remainder of \(7\) (since \(8\times1 = 8\) and \(15 - 8 = 7\)). So \(\frac{15}{8}=1\frac{7}{8}\). The whole number part is \(1\).

Answer:

The whole number is \(1\).