Convert 7.375 To A Fraction: Simple Steps Explained
Table of Contents :
To convert the decimal number 7.375 into a fraction, we will walk you through a series of simple steps that will make the process easy to understand. Whether you're a student, a teacher, or someone simply looking to refine their math skills, this guide will provide you with the necessary information and techniques to accomplish this conversion with confidence. Let's dive in!
Understanding the Basics of Decimals and Fractions
Before we start converting the decimal 7.375 to a fraction, it's essential to understand what decimals and fractions are:
- Decimal: A decimal is a number that represents a fraction of ten. It is based on the decimal system, which uses base 10.
- Fraction: A fraction represents a part of a whole and is composed of a numerator (the top number) and a denominator (the bottom number).
Key Concept: Every decimal can be expressed as a fraction. The goal is to convert 7.375 to its fractional equivalent.
Step-by-Step Conversion Process
Step 1: Identify the Whole Number Part
The first step in converting 7.375 to a fraction is to separate the whole number from the decimal part.
Whole Number: In 7.375, the whole number part is 7.
Step 2: Convert the Decimal Part to a Fraction
Next, we will focus on the decimal part, which is 0.375. To convert this decimal into a fraction, follow these sub-steps:
- Write down the decimal: Start with the decimal part, which is 0.375.
- Determine the place value: Since 0.375 goes to the thousandths place, we can express it as: [ \frac{375}{1000} ] where 375 is the numerator and 1000 is the denominator.
Step 3: Simplify the Fraction
Now we need to simplify the fraction (\frac{375}{1000}) to its lowest terms. To do this, we will find the greatest common divisor (GCD) of 375 and 1000.
Finding the GCD:
- The factors of 375: 1, 3, 5, 15, 25, 75, 125, 375
- The factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
The greatest common divisor here is 125.
Simplifying the Fraction
Now divide both the numerator and the denominator by the GCD:
[ \frac{375 \div 125}{1000 \div 125} = \frac{3}{8} ]
Step 4: Combine the Whole Number and the Fraction
Now that we have converted the decimal part to a simplified fraction, we combine it with the whole number we identified earlier:
So, we have:
[ 7 + \frac{3}{8} = \frac{7 \times 8 + 3}{8} = \frac{56 + 3}{8} = \frac{59}{8} ]
Final Result
The decimal 7.375 can thus be expressed as a fraction in the form:
[ \frac{59}{8} ]
Key Takeaway: The conversion process involves identifying the whole number, converting the decimal part into a fraction, simplifying that fraction, and then combining both parts.
Summary
To summarize the conversion process of 7.375 to a fraction:
| Step | Action | Result |
|---|---|---|
| Identify the whole part | Whole number of 7 | 7 |
| Convert decimal to fraction | Decimal part 0.375 = 375/1000 | 375/1000 |
| Simplify fraction | GCD of 375 and 1000 is 125, thus | 3/8 |
| Combine whole number | 7 + 3/8 | 59/8 |
By following these simple steps, you can convert any decimal number into a fraction with ease. This method not only provides a clear path to conversion but also reinforces your understanding of decimals and fractions, making math more accessible and enjoyable!
Keep practicing, and soon you will find converting decimals to fractions to be a breeze! 🚀