Write \(66\frac{2}{3}\) % as a fraction in simplest form

Explanation

Strategy

We will drop the % symbol and write the given number over 100. Then we will perform the division indicated by the fraction bar and simplify, if possible.

WHY

When writing a percent as a fraction, the numerator and denominator of the fraction should be whole numbers that have no common factors (other than 1).

Solution

• Drop the % symbol and write \(66\frac{2}{3}\) over 100

\(66\frac{2}{3}\)% = \(\frac{66\frac{2}{3}}{100}\)

• The fraction bar indicates division.

\(\frac{66\frac{2}{3}}{100}\) = \(66 \frac{2}{3} \div {100}\)

• Write \(66 \frac{2}{3}\)as a mixed number and then multiply by the reciprocal of 100

= \(\frac{200}{3} \cdot \frac{1}{100} \)

• Multiply the numerators and multiply the denominators

= \( \frac{200 \cdot 1}{3 \cdot 100}\)

• To simplify the fraction, factor 200 as 2 · 100. Then remove the common factor of 100 from the numerator and denominator

= \(\require{cancel} \frac{2 \cdot \cancel{100}^1 \cdot 1}{3 \cdot \cancel{100}_1}\)

= \(\frac{2}{3}\)