write the decimal 86.75 as a fraction or mixed number in simplest form

To write the decimal \(86.75\) as a fraction or mixed number in its simplest form, follow these steps:

1. **Separate the whole number and the decimal part:**
   - The whole number is \(86\).
   - The decimal part is \(0.75\).

2. **Convert \(0.75\) to a fraction:**
   - \(0.75\) can be written as \(\frac{75}{100}\).

3. **Simplify \(\frac{75}{100}\):**
   - Find the greatest common divisor (GCD) of \(75\) and \(100\), which is \(25\).
   - Divide the numerator and the denominator by \(25\):
     \[
     \frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}.
     \]

4. **Combine with the whole number \(86\):**
   - The mixed number is \(86 \frac{3}{4}\).

So, \(86.75\) as a mixed number in simplest form is:

\[
\boxed{86 \frac{3}{4}}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you convert repeating decimals to fractions?
2. What is the process for simplifying fractions?
3. How can you convert a mixed number back into a decimal?
4. How do you convert improper fractions to mixed numbers?
5. What are some tips for finding the GCD of two numbers?

**Tip:** To simplify fractions quickly, divide the numerator and the denominator by their GCD.

Learn how to convert the decimal 86.75 to a mixed number in its simplest form. This step-by-step guide covers converting decimals to fractions, simplifying fractions using the GCD, and combining whole numbers with fractions. Ideal for students in Grades 5-7.

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