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Chapter 5: Problem 75

Write the percent as a fraction or as a mixed number in simplest form. $$ 75 \% $$

Short Answer

Expert verified
The simplest form of 75% as a fraction is \( \frac{3}{4} \).

Step by step solution

01

Write the percent as a fraction

Start by writing the percent (75%) as a fraction. Remember that percent means 'per hundred', so you can write 75% as \( \frac{75}{100} \).
02

Simplify the fraction

Next, simplify the fraction \( \frac{75}{100} \). Both the numerator and denominator can be divided by 25 to simplify the fraction, i.e., \( \frac{75 \div 25}{100 \div 25} \).
03

Final Calculation

When you simplify \( \frac{75 \div 25}{100 \div 25} \), you will get your answer as \( \frac{3}{4} \).

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Key Concepts

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

Percent
Percent is a way to express a number as a fraction of 100. It is denoted using the percent sign (%). When you see 75%, it represents 75 out of 100 or 75 per hundred. This makes it easy to understand proportions and comparisons. For example, if you score 75% on a test, it means you answered 75 out of every 100 questions correctly. Percentages are commonly used in finance, statistics, and many other fields because they provide a straightforward way to represent data.
  • 75% = 75 per 100
  • The sign '%' means "per hundred"
  • Useful for comparing proportions
Fraction
Fractions are mathematical expressions representing a part of a whole. A fraction consists of a numerator and a denominator, separated by a slash. The numerator indicates how many parts are taken, and the denominator shows how many parts make up a whole. When you turn a percent into a fraction, you set the percent number as the numerator and 100 as the denominator. For example, 75% as a fraction is written as \( \frac{75}{100} \).
  • Numerator: Top number indicating parts taken
  • Denominator: Bottom number showing total parts
  • \( 75\% = \frac{75}{100} \)
Simplest Form
To express a fraction in its simplest form, you need to reduce it so that the numerator and denominator are as small as possible, but still represent the same proportion. You do this by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number. Here, for \( \frac{75}{100} \), the GCD is 25. Thus, you simplify by dividing both 75 and 100 by 25:
  • 75 梅 25 = 3
  • 100 梅 25 = 4
So, \( \frac{75}{100} \) simplifies to \( \frac{3}{4} \). This fraction \( \frac{3}{4} \) is in its simplest form.
Mixed Number
A mixed number is a number consisting of both a whole number and a proper fraction. It is used when the numerator of a fraction is larger than the denominator, representing more than a whole. For example, if you had \( \frac{9}{4} \), it would convert to a mixed number like 2 \( \frac{1}{4} \), because 9 divided by 4 is 2 whole parts and a remainder of 1.However, in the case of \( \frac{75}{100} \) simplified to \( \frac{3}{4} \), it does not require conversion into a mixed number as it is already a proper fraction. Understanding the difference between proper fractions and mixed numbers helps in visualizing the amount and size comparisons.

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