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Simplifying a fraction means rewriting it in a way that the numerator and the denominator are as small as possible, while still having the same value as the original fraction. To simplify, you find the greatest common divisor (GCD)—also known as the greatest common factor (GCF)—of the numerator and the denominator and divide both by this number. This process ensures the fraction is reduced to its lowest terms.

For example, if we have the fraction \(\frac{148}{1000}\), we look for the GCD of 148 and 1000, which is 4. By dividing both the numerator and the denominator by 4, we get \(\frac{37}{250}\), which is the simplest form of the original fraction as the numerator and the denominator no longer have any common divisors other than 1.

The GCD of two numbers is the largest positive integer that divides the numbers without leaving a remainder. To determine the GCD, you can use several methods, including listing out the factors of both numbers, using prime factorization, or employing the Euclidean algorithm.

For our example with the fraction \(\frac{148}{1000}\), we need to find the GCD to simplify the fraction. One may list factors or use prime factorization to find that the GCD of 148 and 1000 is 4. Dividing both the numerator and the denominator by this GCD results in the simplified fraction \(\frac{37}{250}\).

To convert a percent to a fraction, you start by writing the percent as a fraction with the percentage number as the numerator and 100 as the denominator, and then simplify. To simplify a fraction, you find the greatest common divisor between the numerator and the denominator and divide them both by it.

For example, when converting 14.8% to a fraction, you would write 14.8% as \(\frac{14.8}{100}\) then get rid of the decimal point by multiplying the numerator and denominator by 10, resulting in \(\frac{148}{1000}\). Finally, to simplify, divide by the GCD of 148 and 1000, which is 4, to get \(\frac{37}{250}\). This is the fraction in its lowest terms.

Converting from a decimal to a fraction involves writing the decimal as a fraction with an appropriate power of 10 as the denominator and then simplifying the resulting fraction. First, count the number of decimal places the decimal has. Multiply and divide the decimal by 10 raised to the number of decimal places to remove the decimal point.

For instance, converting 14.8 (which has one decimal place) to a fraction involves multiplying by 10 to eliminate the decimal point, resulting in \(\frac{148}{10}\). Then, you can further simplify if necessary like converting to \(\frac{148}{1000}\) and then simplifying to \(\frac{37}{250}\) as previously described.