Write each percent as a fraction. Give answers in lowest terms. 7.5%
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Start by understanding that a percentage is a way to express a number as a part of 100. So, 7.5% means 7.5 out of 100.
Write 7.5% as a fraction: .
To eliminate the decimal, multiply both the numerator and the denominator by 10 to get .
Simplify the fraction by finding the greatest common divisor (GCD) of 75 and 1000, which is 25.
Divide both the numerator and the denominator by their GCD: .
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Percentages
A percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol '%'. For example, 7.5% means 7.5 out of 100, which can be represented as the fraction 7.5/100. Understanding percentages is crucial for converting them into fractions.
Fractions
A fraction represents a part of a whole and is expressed as a ratio of two integers, with a numerator (top number) and a denominator (bottom number). To convert a percentage to a fraction, you place the percentage value over 100 and simplify it to its lowest terms. This process is essential for accurately representing percentages in fractional form.
A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. To simplify a fraction, you divide both the numerator and denominator by their greatest common divisor (GCD). This concept is important for ensuring that the fraction is expressed in its simplest form, making it easier to understand and use.