Convert Each Of The Following Percentage Into Fraction In The Lowest Form Like 125%
Introduction
Percentages are a way to express a value as a fraction of 100. However, in many mathematical and real-world applications, it's more convenient to work with fractions in their lowest form. In this article, we'll explore how to convert percentages to fractions in their lowest form, using the example of converting 125% to a fraction.
What is a Percentage?
A percentage is a way to express a value as a fraction of 100. It's denoted by the symbol "%" and is calculated by dividing the value by 100. For example, 25% is equal to 25/100, which can be simplified to 1/4.
Converting Percentages to Fractions
To convert a percentage to a fraction, we can follow these steps:
- Divide the percentage value by 100: This will give us the fraction equivalent of the percentage.
- Simplify the fraction: We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Example: Converting 125% to a Fraction
Let's use the example of converting 125% to a fraction.
Step 1: Divide the percentage value by 100
To convert 125% to a fraction, we can divide 125 by 100.
125 ÷ 100 = 1.25
Step 2: Simplify the fraction
We can simplify the fraction 1.25 by converting it to a mixed number.
1.25 = 1 1/4
Step 3: Convert the mixed number to an improper fraction
We can convert the mixed number 1 1/4 to an improper fraction by multiplying the whole number by the denominator and adding the numerator.
1 × 4 + 1 = 5
So, 1 1/4 is equal to 5/4.
Converting 125% to a Fraction in Lowest Form
We can convert 125% to a fraction in lowest form by dividing both the numerator and the denominator by their GCD.
The GCD of 5 and 4 is 1.
So, 5/4 is already in its lowest form.
Other Examples
Let's try converting some other percentages to fractions in lowest form.
Example 1: Converting 75% to a Fraction
To convert 75% to a fraction, we can follow the same steps as before.
75 ÷ 100 = 0.75
We can simplify the fraction 0.75 by converting it to a mixed number.
0.75 = 3/4
Example 2: Converting 50% to a Fraction
To convert 50% to a fraction, we can follow the same steps as before.
50 ÷ 100 = 0.5
We can simplify the fraction 0.5 by converting it to a mixed number.
0.5 = 1/2
Example 3: Converting 25% to a Fraction
To convert 25% to a fraction, we can follow the same steps as before.
25 ÷ 100 = 0.25
We can simplify the fraction 0.25 by converting it to a mixed number.
0.25 = 1/4
Conclusion
Converting percentages to fractions in lowest form can be a useful skill in mathematics and real-world applications. By following the steps outlined in this article, we can convert percentages to fractions in lowest form, using the example of converting 125% to a fraction. We can also use this skill to convert other percentages to fractions in lowest form.
Common Percentages and Their Fraction Equivalents
Here are some common percentages and their fraction equivalents:
| Percentage | Fraction Equivalent |
|---|---|
| 25% | 1/4 |
| 50% | 1/2 |
| 75% | 3/4 |
| 100% | 1 |
| 125% | 5/4 |
Tips and Tricks
Here are some tips and tricks for converting percentages to fractions in lowest form:
- Use a calculator: If you're having trouble converting a percentage to a fraction, you can use a calculator to get an approximate value.
- Simplify the fraction: Once you've converted a percentage to a fraction, make sure to simplify the fraction by dividing both the numerator and the denominator by their GCD.
- Use a mixed number: If you're having trouble converting a percentage to a fraction, you can try converting it to a mixed number first.
Conclusion
Introduction
In our previous article, we explored how to convert percentages to fractions in lowest form. In this article, we'll answer some common questions about converting percentages to fractions in lowest form.
Q: What is the difference between a percentage and a fraction?
A: A percentage is a way to express a value as a fraction of 100. It's denoted by the symbol "%" and is calculated by dividing the value by 100. A fraction, on the other hand, is a way to express a value as a ratio of two numbers.
Q: How do I convert a percentage to a fraction?
A: To convert a percentage to a fraction, you can follow these steps:
- Divide the percentage value by 100: This will give you the fraction equivalent of the percentage.
- Simplify the fraction: You can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder.
Q: How do I simplify a fraction?
A: To simplify a fraction, you can follow these steps:
- Find the GCD: Find the greatest common divisor of the numerator and the denominator.
- Divide both numbers by the GCD: Divide both the numerator and the denominator by the GCD.
Q: What is a mixed number?
A: A mixed number is a way to express a fraction as a combination of a whole number and a fraction. For example, 2 1/4 is a mixed number.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, you can follow these steps:
- Multiply the whole number by the denominator: Multiply the whole number by the denominator.
- Add the numerator: Add the numerator to the result.
- Write the result as an improper fraction: Write the result as an improper fraction.
Q: What is an improper fraction?
A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Q: How do I convert an improper fraction to a mixed number?
A: To convert an improper fraction to a mixed number, you can follow these steps:
- Divide the numerator by the denominator: Divide the numerator by the denominator.
- Write the result as a mixed number: Write the result as a mixed number.
Q: What are some common percentages and their fraction equivalents?
A: Here are some common percentages and their fraction equivalents:
| Percentage | Fraction Equivalent |
|---|---|
| 25% | 1/4 |
| 50% | 1/2 |
| 75% | 3/4 |
| 100% | 1 |
| 125% | 5/4 |
Q: How do I use a calculator to convert a percentage to a fraction?
A: To use a calculator to convert a percentage to a fraction, you can follow these steps:
- Enter the percentage value: Enter the percentage value into the calculator.
- Divide by 100: Divide the percentage value by 100.
- Simplify the fraction: Simplify the fraction by dividing both the numerator and the denominator by their GCD.
Conclusion
Converting percentages to fractions in lowest form can be a useful skill in mathematics and real-world applications. By following the steps outlined in this article, we can convert percentages to fractions in lowest form, using the example of converting 125% to a fraction. We can also use this skill to convert other percentages to fractions in lowest form.