Write 175% as a fraction in simplest form

Explanation

Strategy We will drop the % symbol and write each given number over 100.Then we will simplify the resulting fraction, if possible.

WHY Percent means parts per one hundred and the word per indicates a ratio (fraction).

• Drop the % symbol and write 175 over 100

175% = \(\frac{175}{100}\)

• To simplify the fraction, prime factor 175 and 100. Remove the common factors of 5 from the numerator and denominator.

= \(\require{cancel}\frac{\cancel{5}^1 \cdot \cancel{5}^1 \cdot 7}{2 \cdot 2 \cdot \cancel{5}_1 \cdot \cancel{5}_1}\)

= \(\frac{7}{4}\)

Thus, 175% = \(\frac{7}{4}\)