Convert 71 2/3 % to a fraction in lowest terms.

The Correct Answer and Explanation is:

To convert 71 2/3% to a fraction in lowest terms:

Correct Answer:

4360\boxed{\frac{43}{60}}

Detailed Explanation (300+ words):

Converting a percent to a fraction in lowest terms involves a few systematic steps. Let’s walk through them carefully using 71 2/3% as an example.

Step 1: Convert the mixed number percent to an improper fraction

The percentage given is a mixed number: 7123%71 \frac{2}{3}\%

First, convert this mixed number to an improper fraction.

To do that, multiply the whole number part (71) by the denominator of the fractional part (3) and then add the numerator: 71×3=213213+2=21571 \times 3 = 213 \\ 213 + 2 = 215

So: 7123=215371 \frac{2}{3} = \frac{215}{3}

Step 2: Convert the percent to a fraction

Remember that percent means “per hundred”, so we divide the number by 100: 2153÷100=2153×1100=215300\frac{215}{3} \div 100 = \frac{215}{3} \times \frac{1}{100} = \frac{215}{300}

Now we simplify the fraction 215300\frac{215}{300}.

Step 3: Simplify the fraction

To reduce 215300\frac{215}{300}, we find the greatest common divisor (GCD) of the numerator and denominator.

Prime factorization of 215: 215=5×43215 = 5 \times 43
Prime factorization of 300: 300=22×3×52300 = 2^2 \times 3 \times 5^2

The common factor is 5.

Divide both numerator and denominator by 5: 215÷5300÷5=4360\frac{215 \div 5}{300 \div 5} = \frac{43}{60}

Final Answer: