Write The Fraction As A Percent. Write The Percent Using Both Fractions And Decimals.\[$\frac{3}{8}\$\]The Percent Written Using Fractions Is \[$\square\$\] \[$\%\$\].(Simplify Your Answer. Type An Integer, Proper Fraction, Or

by ADMIN 227 views

Introduction

In mathematics, converting fractions to percentages is a fundamental concept that is essential for various applications, including finance, science, and engineering. The ability to express a fraction as a percentage is crucial for comparing and analyzing data, making informed decisions, and solving problems. In this article, we will explore the process of converting fractions to percentages, using both fractions and decimals.

Understanding Fractions and Percentages

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the number on top) and a denominator (the number on the bottom). For example, the fraction 38\frac{3}{8} represents three-eighths of a whole.

A percentage, on the other hand, is a way of expressing a value as a fraction of 100. It is denoted by the symbol "%". For example, 25% is equal to 25100\frac{25}{100}.

Converting Fractions to Percentages

To convert a fraction to a percentage, we need to divide the numerator by the denominator and multiply the result by 100. This can be expressed mathematically as:

abΓ—100=aΓ—100b\frac{a}{b} \times 100 = \frac{a \times 100}{b}

where aa is the numerator and bb is the denominator.

Example: Converting 38\frac{3}{8} to a Percentage

Using the formula above, we can convert the fraction 38\frac{3}{8} to a percentage as follows:

38Γ—100=3Γ—1008=3008=37.5%\frac{3}{8} \times 100 = \frac{3 \times 100}{8} = \frac{300}{8} = 37.5\%

Therefore, the percentage written using fractions is 37.5%\boxed{37.5\%}.

Converting Percentages to Fractions

To convert a percentage to a fraction, we need to divide the percentage value by 100 and simplify the result. This can be expressed mathematically as:

a100=ab\frac{a}{100} = \frac{a}{b}

where aa is the percentage value and bb is the denominator.

Example: Converting 37.5% to a Fraction

Using the formula above, we can convert the percentage 37.5% to a fraction as follows:

37.5100=38\frac{37.5}{100} = \frac{3}{8}

Therefore, the fraction equivalent of 37.5% is 38\boxed{\frac{3}{8}}.

Converting Percentages to Decimals

To convert a percentage to a decimal, we need to divide the percentage value by 100. This can be expressed mathematically as:

a100=aΓ—0.01\frac{a}{100} = a \times 0.01

where aa is the percentage value.

Example: Converting 37.5% to a Decimal

Using the formula above, we can convert the percentage 37.5% to a decimal as follows:

37.5100=0.375\frac{37.5}{100} = 0.375

Therefore, the decimal equivalent of 37.5% is 0.375\boxed{0.375}.

Conclusion

In conclusion, converting fractions to percentages is a straightforward process that involves dividing the numerator by the denominator and multiplying the result by 100. We can also convert percentages to fractions and decimals using simple mathematical formulas. By understanding these concepts, we can express values in different forms and make informed decisions in various applications.

Common Fractions and Their Equivalent Percentages

Here are some common fractions and their equivalent percentages:

Fraction Percentage
12\frac{1}{2} 50%
14\frac{1}{4} 25%
34\frac{3}{4} 75%
23\frac{2}{3} 66.67%
35\frac{3}{5} 60%
45\frac{4}{5} 80%

Common Percentages and Their Equivalent Fractions

Here are some common percentages and their equivalent fractions:

Percentage Fraction
50% 12\frac{1}{2}
25% 14\frac{1}{4}
75% 34\frac{3}{4}
66.67% 23\frac{2}{3}
60% 35\frac{3}{5}
80% 45\frac{4}{5}

Common Percentages and Their Equivalent Decimals

Here are some common percentages and their equivalent decimals:

Percentage Decimal
50% 0.5
25% 0.25
75% 0.75
66.67% 0.6667
60% 0.6
80% 0.8

Q: What is the formula for converting a fraction to a percentage?

A: The formula for converting a fraction to a percentage is:

abΓ—100=aΓ—100b\frac{a}{b} \times 100 = \frac{a \times 100}{b}

where aa is the numerator and bb is the denominator.

Q: How do I convert a percentage to a fraction?

A: To convert a percentage to a fraction, divide the percentage value by 100 and simplify the result. For example, to convert 37.5% to a fraction, divide 37.5 by 100 and simplify:

37.5100=38\frac{37.5}{100} = \frac{3}{8}

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, divide the percentage value by 100. For example, to convert 37.5% to a decimal, divide 37.5 by 100:

37.5100=0.375\frac{37.5}{100} = 0.375

Q: What is the difference between a fraction and a percentage?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a percentage is a way of expressing a value as a fraction of 100.

Q: Can I convert a decimal to a percentage?

A: Yes, you can convert a decimal to a percentage by multiplying the decimal value by 100. For example, to convert 0.375 to a percentage, multiply 0.375 by 100:

0.375Γ—100=37.5%0.375 \times 100 = 37.5\%

Q: Can I convert a percentage to a decimal?

A: Yes, you can convert a percentage to a decimal by dividing the percentage value by 100. For example, to convert 37.5% to a decimal, divide 37.5 by 100:

37.5100=0.375\frac{37.5}{100} = 0.375

Q: How do I simplify a fraction?

A: To simplify a fraction, divide the numerator and denominator by their greatest common divisor (GCD). For example, to simplify the fraction 1216\frac{12}{16}, divide both numbers by their GCD, which is 4:

1216=34\frac{12}{16} = \frac{3}{4}

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers, including:

  • Listing the factors of each number and finding the greatest common factor
  • Using the Euclidean algorithm
  • Using a calculator or online tool

Q: Can I convert a mixed number to a percentage?

A: Yes, you can convert a mixed number to a percentage by converting the whole number part to a decimal, multiplying the decimal value by the fraction part, and then multiplying the result by 100. For example, to convert the mixed number 2 12\frac{1}{2} to a percentage, convert the whole number part to a decimal, multiply the decimal value by the fraction part, and then multiply the result by 100:

2Γ—1=22 \times 1 = 2

2Γ—12=12 \times \frac{1}{2} = 1

1Γ—100=100%1 \times 100 = 100\%

Q: Can I convert a percentage to a mixed number?

A: Yes, you can convert a percentage to a mixed number by dividing the percentage value by 100 and then converting the decimal value to a mixed number. For example, to convert the percentage 37.5% to a mixed number, divide 37.5 by 100 and then convert the decimal value to a mixed number:

37.5100=0.375\frac{37.5}{100} = 0.375

0.375=0.3+0.0750.375 = 0.3 + 0.075

0.3=3100.3 = \frac{3}{10}

0.075=3400.075 = \frac{3}{40}

310+340=1240+340=1540=38\frac{3}{10} + \frac{3}{40} = \frac{12}{40} + \frac{3}{40} = \frac{15}{40} = \frac{3}{8}

Therefore, the mixed number equivalent of 37.5% is 3 38\frac{3}{8}.