Converting decimals into fractions can seem intimidating at first, but with a bit of practice and understanding, it becomes an incredibly easy task! In this post, we'll tackle how to convert 87.5 into a fraction with five simple steps. Whether you're a student brushing up on your math skills or someone who just wants to understand fractions better, this guide is for you. Let's break it down! 📚✨
Step 1: Understand the Decimal
First off, it's essential to understand what the decimal number 87.5 represents. The number 87.5 consists of two parts: the whole number part (87) and the decimal part (0.5). In fraction terms, this is equivalent to having 87 whole units plus an additional half.
Step 2: Convert the Decimal to a Fraction
Next, let’s convert the decimal part (0.5) into a fraction. The number 0.5 is the same as 5 tenths (5/10) since it is one-half of a whole. So we can now express 87.5 as:
[ 87.5 = 87 + 0.5 = 87 + \frac{5}{10} ]
Step 3: Write as a Single Fraction
To combine the whole number and the fractional part, we need a common denominator. The whole number 87 can be expressed as a fraction too. To do that, we can write 87 as 87/1 and make its denominator 10.
Here’s how:
[ 87 = \frac{87 \times 10}{1 \times 10} = \frac{870}{10} ]
Now, we can add the two fractions together:
[ 87.5 = \frac{870}{10} + \frac{5}{10} = \frac{870 + 5}{10} = \frac{875}{10} ]
Step 4: Simplify the Fraction
Now that we have the fraction (\frac{875}{10}), our next step is to simplify it. We look for the greatest common divisor (GCD) of the numerator (875) and the denominator (10). In this case, the GCD is 5.
To simplify, we divide both the numerator and the denominator by their GCD:
[ \frac{875 \div 5}{10 \div 5} = \frac{175}{2} ]
So, the simplified fraction is (\frac{175}{2}).
Step 5: Final Representation
Finally, it's useful to express this in different forms:
- Improper Fraction: ( \frac{175}{2} )
- Mixed Number: If you prefer it in mixed number form, divide 175 by 2, which gives us 87 with a remainder of 1. Therefore, the mixed number is ( 87 \frac{1}{2} ).
And there you have it! Converting the decimal 87.5 into a fraction involves these five straightforward steps. Let’s wrap up with some common mistakes to avoid when performing decimal to fraction conversions.
Common Mistakes to Avoid
- Misunderstanding the Decimal: Ensure you grasp the meaning of the decimal parts accurately.
- Forgetting to Simplify: Always check if the fraction can be simplified further for the cleanest answer.
- Skipping the Mixed Number Form: Sometimes, converting to a mixed number makes it easier to understand the value.
Troubleshooting Tips
- Check Your Work: After performing the conversion, double-check your steps.
- Use Calculators When Needed: Don’t hesitate to use a calculator for the division step if you’re unsure.
- Practice More: The more you practice, the more comfortable you'll become with the process.
<div class="faq-section"> <div class="faq-container"> <h2>Frequently Asked Questions</h2> <div class="faq-item"> <div class="faq-question"> <h3>Can all decimals be converted to fractions?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Yes, all terminating decimals (like 87.5) can be converted to fractions. Non-terminating decimals can be converted to fractions as well, but it requires more advanced techniques.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>What is a mixed number?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>A mixed number is a whole number combined with a proper fraction. For example, 87.5 can be expressed as ( 87 \frac{1}{2} ).</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>Why is it important to simplify fractions?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Simplifying fractions makes them easier to read and understand, and it can help you see the relationship between numbers more clearly.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>How do I convert a repeating decimal to a fraction?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>To convert a repeating decimal to a fraction, you generally set up an equation to represent the decimal, multiply to eliminate the repeating part, and then solve for the fraction.</p> </div> </div> </div> </div>
Wrapping it up, converting 87.5 to a fraction is really all about understanding the steps involved. With practice, you can make this a quick and easy task. Don’t hesitate to check back for more tutorials and keep honing your skills!
<p class="pro-note">✨Pro Tip: Practice makes perfect! The more you work with decimals and fractions, the easier it will become!</p>