Rewrite this percent problem as a fraction problem in simplest terms.
Find $20 \%$ of 30.
Find [ ]/[ ] of 30.
To represent a percentage as a fraction, we use the definition of a percent, which is "per hundred." Therefore, 20% is equivalent to the ratio 20 out of 100, which can be written as the fraction \(\frac{20}{100}\). Our objective is to simplify this fraction to its lowest terms.
To simplify the fraction \(\frac{20}{100}\), we find the greatest common divisor (GCD) of both the numerator (20) and the denominator (100). Both numbers are divisible by 20. Dividing the numerator by 20 gives \(20 \div 20 = 1\), and dividing the denominator by 20 gives \(100 \div 20 = 5\). Thus, the fraction \(\frac{20}{100}\) simplifies to \(\frac{1}{5}\).
Now that we have the simplest form of the fraction, we can express the original problem "20% of 30" as "1/5 of 30". Performing the multiplication, we calculate \(\frac{1}{5} \times 30 = \frac{30}{5} = 6\). However, the specific task was to write the problem as a fraction of 30. Therefore, the simplified fraction to be placed in the box is \(\frac{1}{5}\).
Understanding how to convert percentages to fractions is essential in daily life, such as when calculating discounts at a store. For example, if an item costs \$30 and is 20% off, knowing that 20% is the same as the fraction \(\frac{1}{5}\) allows you to quickly calculate the discount: \(\frac{1}{5} \times \$30 = \$6\). This makes mental math much easier and helps in making quick shopping decisions!