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Write each percent as a fraction in lowest terms. $$65 \frac{1}{4} \%$$

Short Answer

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Question: Convert the mixed number percentage $$65\frac{1}{4}\%$$ to a fraction in its lowest terms. Answer: $$\frac{261}{400}$$

Step by step solution

01

Convert mixed number to an improper fraction

To convert the mixed number percentage $$65 \frac{1}{4}\%$$ to an improper fraction, we multiply the whole number by the denominator and add the numerator. Then, we place the result over the original denominator: $$65 \times 4 + 1 = 261$$ So the improper fraction is $$\frac{261}{4}\%$$
02

Convert the improper fraction to a decimal

To convert the percentage to a decimal, we divide the numerator by the denominator and multiply the result by 100: $$\frac{261}{4} \div 100 = \frac{261}{400}$$
03

Convert the decimal to a fraction

Now we have the fraction $$\frac{261}{400}$$, which represents the decimal form of the given percentage.
04

Simplify the fraction to its lowest terms

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (261) and the denominator (400). The GCD is 1, which means the fraction is already in its simplest form: $$\frac{261}{400}$$ So, $$65\frac{1}{4}\%$$ can be written as the fraction $$\frac{261}{400}$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converting Mixed Numbers to Improper Fractions
Understanding how to convert mixed numbers to improper fractions is a key skill in mathematics, and it's particularly useful when dealing with percentages. A mixed number includes both a whole number and a fraction, such as \(65\frac{1}{4}\).

To convert a mixed number to an improper fraction, you start by multiplying the whole number by the denominator of the fraction. In our example, multiply 65 (the whole number) by 4 (the denominator of the fraction part) to get 260. Then, add the numerator of the fraction, which is 1, giving us 261. This value becomes the numerator of the improper fraction, while the denominator remains the same, so we have \(\frac{261}{4}\).

This conversion is essential when you want to convert a mixed number percentage into an easier form to work with, such as when simplifying or when converting to a decimal.
Simplifying Fractions
Simplifying fractions is a process of reducing a fraction to its lowest terms. To simplify a fraction, you need to find the greatest common divisor (GCD) of both the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.

Once the GCD is found, you divide both the numerator and the denominator by this number. If the GCD is 1, that means the fraction is already in its simplest form. For instance, the fraction \(\frac{261}{400}\) already has a GCD of 1, indicating it cannot be simplified further.

Understanding simplification allows students to recognize fractions that represent the same value and can be especially helpful in solving problems that involve fraction comparisons or combinations.
Percent to Decimal Conversion
Percent to decimal conversion is another foundational math skill. To convert a percentage to a decimal, remember that 'percent' means 'per hundred'. Therefore, you convert percentages to decimals by dividing the percentage by 100.

For example, to convert the percentage \(65\frac{1}{4}\%\) to a decimal, you first transform the mixed number into an improper fraction (which gives us \(\frac{261}{4}\%\)) and then divide by 100. This gives you \(\frac{261}{400}\), which is the decimal representation of the percentage.

Mastering this conversion process makes it easier for students to perform calculations that involve percentages, whether it's for financial calculations, assessing probabilities, or working with growth rates in science and social studies.

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