Fractions, decimals, and percentages are three different ways of expressing the same value. This article provides a comprehensive guide to understanding and converting between these three representations.

### Key Facts

- Equivalents: Fractions, decimals, and percentages are different ways of expressing the same value. For example, 1/2 is equivalent to 0.5 as a decimal and 50% as a percentage.
- Converting Percentages to Decimals: To convert a percentage to a decimal, divide by 100 and remove the percent sign. For example, 75% is equivalent to 0.75 as a decimal.
- Converting Decimals to Percentages: To convert a decimal to a percentage, multiply by 100 and add the percent sign. For example, 0.25 is equivalent to 25%.
- Converting Fractions to Decimals: To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For example, 3/4 is equal to 0.75 as a decimal.
- Converting Decimals to Fractions: To convert a decimal to a fraction, write the decimal as the numerator and 1 as the denominator. Then, simplify the fraction if possible. For example, 0.5 is equal to 1/2.
- Converting Fractions to Percentages: To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100 and add the percent sign. For example, 3/8 is equal to 37.5%.
- Converting Percentages to Fractions: To convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction if possible. For example, 80% is equal to 4/5.

### Equivalents

Fractions, decimals, and percentages are equivalent to each other. This means that they represent the same quantity, just in different forms. For example, the fraction 1/2 is equivalent to the decimal 0.5 and the percentage 50%.

### Converting Percentages to Decimals

To convert a percentage to a decimal, divide the percentage by 100 and remove the percent sign. For instance, 75% is equivalent to 0.75 as a decimal.

### Converting Decimals to Percentages

To convert a decimal to a percentage, multiply the decimal by 100 and add the percent sign. For instance, 0.25 is equivalent to 25% as a percentage.

### Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For instance, 3/4 is equal to 0.75 as a decimal.

### Converting Decimals to Fractions

To convert a decimal to a fraction, write the decimal as the numerator and 1 as the denominator. Then, simplify the fraction if possible. For instance, 0.5 is equal to 1/2.

### Converting Fractions to Percentages

To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100 and add the percent sign. For instance, 3/8 is equal to 37.5% as a percentage.

### Converting Percentages to Fractions

To convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction if possible. For instance, 80% is equal to 4/5 as a fraction.

### Conclusion

Fractions, decimals, and percentages are all valid representations of quantities. Understanding how to convert between these representations is essential for various mathematical and scientific applications.

## FAQs

### What are fractions, decimals, and percentages?

Fractions, decimals, and percentages are different ways of expressing the same value. A fraction is a part of a whole, a decimal is a number written using a decimal point, and a percentage is a value expressed as a fraction of 100.

### How do I convert a fraction to a decimal?

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). For example, to convert 3/4 to a decimal, divide 3 by 4, which gives you 0.75.

### How do I convert a decimal to a percentage?

To convert a decimal to a percentage, multiply the decimal by 100 and add the percent sign. For example, to convert 0.25 to a percentage, multiply 0.25 by 100, which gives you 25%.

### How do I convert a percentage to a fraction?

To convert a percentage to a fraction, divide the percentage by 100 and simplify the fraction if possible. For example, to convert 75% to a fraction, divide 75 by 100, which gives you 3/4.

### How do I convert a fraction to a percentage?

To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100 and add the percent sign. For example, to convert 3/8 to a percentage, divide 3 by 8, which gives you 0.375. Then, multiply 0.375 by 100, which gives you 37.5%.

### How do I simplify a fraction?

To simplify a fraction, divide both the numerator and the denominator by their greatest common factor (GCF). For example, to simplify 6/12, divide both 6 and 12 by 6, which gives you 1/2.

### What is the difference between a proper fraction and an improper fraction?

A proper fraction is a fraction where the numerator is smaller than the denominator. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

### What is a mixed number?

A mixed number is a number that consists of a whole number and a fraction. For example, 2 1/2 is a mixed number.