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Chapter 0: Problem 171

Write each percent as a fraction. Give answers in lowest terms. See Example 13. $$ 51 \% $$

Short Answer

Expert verified
51% = \[ \frac{51}{100} \]

Step by step solution

01

- Understand Percent

Percent means per hundred. Therefore, 51% means 51 out of 100.
02

- Write as Fraction

Write 51% as a fraction: \[ \frac{51}{100} \]
03

- Simplify the Fraction

Check if the fraction \[ \frac{51}{100} \] can be simplified. The greatest common divisor (GCD) of 51 and 100 is 1, so the fraction is already in its lowest terms.

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Key Concepts

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

Percent
Percentages are a way of expressing a number as a part of 100. The word 'percent' comes from the Latin words 'per centum,' which mean 'by the hundred.'
For example, if you have 51 apples out of 100, you can say you have 51 percent of the apples.
This can be written as 51%.
Fraction
A fraction represents a part of a whole. It is written with two numbers separated by a slash.
There is a numerator (the top number) and a denominator (the bottom number). The numerator represents how many parts we have, and the denominator shows the total number of parts.
When converting from a percent to a fraction, you place the percent number over 100. For example, 51% becomes the fraction \(\frac{51}{100}\).
Simplifying Fractions
Simplifying a fraction means to reduce it to its simplest form.
The simplest form of a fraction has the smallest possible numerator and denominator while keeping the same value.
To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator.
The GCD is the largest number that divides both the numerator and the denominator without any remainder.
When converting 51% to a fraction, you get \[ \frac{51}{100} \].
Since the GCD of 51 and 100 is 1, the fraction is already in its simplest form.

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