Question

divide. write the answer in simplest form.
$1\frac{3}{7} \div \frac{2}{3} = \square$

Explanation:

Step1: Convert mixed number to improper fraction

To convert \(1\frac{3}{7}\) to an improper fraction, we use the formula: \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(1\frac{3}{7}=\frac{1\times7 + 3}{7}=\frac{10}{7}\).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\). So, \(\frac{10}{7}\div\frac{2}{3}=\frac{10}{7}\times\frac{3}{2}\).

Step3: Multiply the fractions

Multiply the numerators and denominators: \(\frac{10\times3}{7\times2}=\frac{30}{14}\).

Step4: Simplify the fraction

Simplify \(\frac{30}{14}\) by dividing numerator and denominator by their greatest common divisor, which is 2. So, \(\frac{30\div2}{14\div2}=\frac{15}{7}\), or as a mixed number \(2\frac{1}{7}\). But since the problem says "simplest form", an improper fraction or mixed number is acceptable, but \(\frac{15}{7}\) is also correct. Wait, let's check the multiplication again. \(10\times3 = 30\), \(7\times2 = 14\), then \(\frac{30}{14}\) simplifies to \(\frac{15}{7}\) (dividing numerator and denominator by 2). Alternatively, \(\frac{15}{7}=2\frac{1}{7}\). But let's do the multiplication step again: \(\frac{10}{7}\times\frac{3}{2}\), 10 and 2 can be simplified first. 10 divided by 2 is 5, 2 divided by 2 is 1. So, \(\frac{5\times3}{7\times1}=\frac{15}{7}\). Yep, that's simpler. So the result is \(\frac{15}{7}\) or \(2\frac{1}{7}\). But let's confirm: \(\frac{10}{7}\times\frac{3}{2}=\frac{10\times3}{7\times2}=\frac{30}{14}=\frac{15}{7}\).

Answer:

\(\frac{15}{7}\) (or \(2\frac{1}{7}\))