To find [tex]\( 7 \frac{1}{3} \div 2 \frac{1}{5} \)[/tex] and simplify the answer, follow these steps:
### Step 1: Convert the Mixed Numbers to Improper Fractions
First, convert the mixed numbers into improper fractions.
- For [tex]\( 7 \frac{1}{3} \:
\[
7 \frac{1}{3} = 7 + \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{22}{3}
\]
- For \( 2 \frac{1}{5} \:
\[
2 \frac{1}{5} = 2 + \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}
\]
### Step 2: Divide the Fractions
To divide fractions, multiply by the reciprocal of the divisor.
So, we calculate \(\frac{22}{3} \div \frac{11}{5}\)[/tex]:
[tex]\[
\frac{22}{3} \div \frac{11}{5} = \frac{22}{3} \times \frac{5}{11}
\][/tex]
### Step 3: Perform the Multiplication
Multiply the numerators and the denominators:
[tex]\[
\frac{22 \times 5}{3 \times 11} = \frac{110}{33}
\][/tex]
### Step 4: Simplify the Fraction
Simplify [tex]\(\frac{110}{33}\)[/tex] by finding the greatest common divisor (GCD) of 110 and 33, which is 11.
[tex]\[
\frac{110 \div 11}{33 \div 11} = \frac{10}{3}
\][/tex]
### Step 5: Convert the Improper Fraction to a Mixed Number
Convert [tex]\(\frac{10}{3}\)[/tex] to a mixed number by dividing the numerator by the denominator.
[tex]\[
10 \div 3 = 3 \text{ remainder } 1
\][/tex]
So, [tex]\(\frac{10}{3}\)[/tex] is [tex]\(3\frac{1}{3}\)[/tex].
Thus, the answer to [tex]\( 7 \frac{1}{3} \div 2 \frac{1}{5} \)[/tex] is [tex]\(\boxed{3 \frac{1}{3}}\)[/tex].
