Question

express 175% as a fraction in simplest form.

• $\frac{4}{7}$
• $\frac{10}{175}$
• $\frac{7}{4}$
• $\frac{35}{20}$

Explanation:

Step1: Recall percentage to fraction conversion

To convert a percentage to a fraction, we divide the percentage value by 100. So, \(175\%=\frac{175}{100}\).

Step2: Simplify the fraction

We find the greatest common divisor (GCD) of 175 and 100. The factors of 175 are \(1, 5, 7, 25, 35, 175\) and the factors of 100 are \(1, 2, 4, 5, 10, 20, 25, 50, 100\). The GCD of 175 and 100 is 25.
Divide both the numerator and the denominator by 25: \(\frac{175\div25}{100\div25}=\frac{7}{4}\)? Wait, no, wait. Wait, 175 divided by 25 is 7, 100 divided by 25 is 4. Wait, but let's check the options. Wait, maybe I made a mistake. Wait, 175% is \(1.75\) as a decimal. \(1.75=\frac{175}{100}=\frac{7}{4}\) when simplified? Wait, but let's check the options. The options are \(\frac{4}{7}\), \(\frac{10}{175}\), \(\frac{7}{4}\), \(\frac{35}{20}\). Wait, \(\frac{35}{20}\) simplifies to \(\frac{7}{4}\) (divide numerator and denominator by 5: \(35\div5 = 7\), \(20\div5=4\)). And \(\frac{7}{4}\) is equal to \(1.75\) which is \(175\%\). Let's check the other options: \(\frac{4}{7}\approx0.571\), \(\frac{10}{175}=\frac{2}{35}\approx0.057\), \(\frac{7}{4} = 1.75=175\%\), \(\frac{35}{20}=\frac{7}{4}\). So the correct answer should be \(\frac{7}{4}\) (or \(\frac{35}{20}\) which simplifies to \(\frac{7}{4}\)). Wait, maybe the initial thought had a miscalculation. Let's re - do:

\(175\%=\frac{175}{100}\). Divide numerator and denominator by 25: \(\frac{175\div25}{100\div25}=\frac{7}{4}\). And \(\frac{35}{20}\) can be simplified by dividing numerator and denominator by 5: \(\frac{35\div5}{20\div5}=\frac{7}{4}\). So the correct fraction in simplest form is \(\frac{7}{4}\), which is one of the options (the third option, \(\frac{7}{4}\), or the fourth option \(\frac{35}{20}\) which is equivalent to \(\frac{7}{4}\)).

Wait, maybe the original problem's options: let's list them again. The options are:

• \(\frac{4}{7}\)

• \(\frac{10}{175}\)

• \(\frac{7}{4}\)

• \(\frac{35}{20}\)

So to find the correct one, we convert \(175\%\) to fraction:

\(175\%=\frac{175}{100}=\frac{7}{4}\) (after dividing numerator and denominator by 25). Also, \(\frac{35}{20}\) simplifies to \(\frac{7}{4}\) (divide numerator and denominator by 5: \(35\div5 = 7\), \(20\div5 = 4\)). So the correct answer is the option with \(\frac{7}{4}\) (the third option) or \(\frac{35}{20}\) (the fourth option, which is equivalent). But let's check the options again. The options are:

1. \(\frac{4}{7}\)

1. \(\frac{10}{175}\)

1. \(\frac{7}{4}\)

1. \(\frac{35}{20}\)

So the correct answer is the option with \(\frac{7}{4}\) (third option) or \(\frac{35}{20}\) (fourth option, as it simplifies to \(\frac{7}{4}\)). But let's confirm:

\(175\% = 1.75=\frac{7}{4}\) (since \(4\times1.75 = 7\)). And \(\frac{35}{20}=\frac{7}{4}\) (because \(35\div5 = 7\), \(20\div5 = 4\)). So the correct answer is the option with \(\frac{7}{4}\) (third option) or \(\frac{35}{20}\) (fourth option). But looking at the options, the third option is \(\frac{7}{4}\), which is the simplified form.

Answer:

The correct option is \(\frac{7}{4}\) (the third option in the given choices, i.e., the option with \(\frac{7}{4}\)).