How Do you Write 375% as a Fraction or Mixed Number in Simplest form?

Converting percentages to fractions or mixed numbers is a fundamental skill in mathematics. In this blog post, we’ll explore how to write 375% as a fraction or mixed number in simplest form, step by step.

How Do you Write 375% as a Fraction or Mixed Number in Simplest form?

To write 375% as a fraction in simplest form, you convert it to 375/100, which simplifies to 15/4. To express it as a mixed number, divide the numerator (15) by the denominator (4), resulting in 3 with a remainder of 3. This becomes the fraction 3/4. So, 375% is equivalent to the mixed number 3 3/4 in simplest form.

Understanding Percentages

Before we delve into converting percentages to fractions or mixed numbers, let’s ensure we understand what percentages are. Percentages, denoted by the symbol “%,” are a way of expressing a portion of a whole in terms of 100 parts. For example, 50% represents half (or 50 out of 100 parts) of a whole.

Converting Percentages to Fractions

To convert a percentage to a fraction, you follow these steps:

Step 1: Write the Percentage as a Fraction Over 100

In this case, we want to convert 375% into a fraction. So, we write it as:

375% = 375/100

Step 2: Simplify the Fraction

Now that we have 375/100, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator (375) and the denominator (100) and dividing both by that value. In this case, the GCD is 25:

(375 ÷ 25) / (100 ÷ 25) = 15/4

So, 375% is equivalent to the fraction 15/4.

Converting Fractions to Mixed Numbers

Now that we have 15/4 as our fraction, we can convert it to a mixed number. A mixed number consists of a whole number part and a proper fraction part. Here’s how you do it:

Step 3: Divide the Numerator by the Denominator

Divide the numerator (15) by the denominator (4):

15 ÷ 4 = 3 with a remainder of 3.

Step 4: Express the Remainder as a Fraction

The remainder, 3, becomes the numerator of the proper fraction part, and the denominator remains the same (4):

3/4

Step 5: Combine the Whole Number and Fraction

Now, combine the whole number (3) and the proper fraction (3/4) to form the mixed number:

3 3/4

So, 375% can be expressed as the mixed number 3 3/4 in simplest form.

Summary

In summary, converting percentages to fractions and then to mixed numbers involves simple steps. First, write the percentage as a fraction over 100. Then, simplify the fraction if possible. Finally, convert the fraction to a mixed number by dividing the numerator by the denominator, expressing any remainder as a proper fraction. In the case of 375%, it simplifies to the mixed number 3 3/4. Understanding these conversion techniques is essential for various math and real-life applications.