19.875 converted to mixed fraction with steps

To convert the decimal \( 19.875 \) to a mixed fraction, follow these steps:

### Step 1: Separate the whole number from the decimal.
The given decimal number is \( 19.875 \).
- **Whole number part:** \( 19 \)
- **Decimal part:** \( 0.875 \)

### Step 2: Convert the decimal part to a fraction.
We need to convert \( 0.875 \) to a fraction.

1. Write \( 0.875 \) as a fraction: 
   \[
   0.875 = \frac{875}{1000}
   \]

2. Simplify the fraction by finding the greatest common divisor (GCD) of 875 and 1000. 

   The GCD of 875 and 1000 is 125. So, divide both the numerator and the denominator by 125:
   \[
   \frac{875 \div 125}{1000 \div 125} = \frac{7}{8}
   \]

Thus, \( 0.875 = \frac{7}{8} \).

### Step 3: Combine the whole number and the fraction.
Now, combine the whole number part \( 19 \) with the fraction \( \frac{7}{8} \) to form the mixed fraction:
\[
19.875 = 19 \frac{7}{8}
\]

### Final Answer:
The decimal \( 19.875 \) as a mixed fraction is \( 19 \frac{7}{8} \).

Would you like more details on any of the steps? Here are five related questions you might consider:

1. How do you convert repeating decimals to fractions?
2. What is the process to find the GCD of two numbers?
3. How can we convert improper fractions to mixed numbers?
4. What are some other examples of converting decimals to fractions?
5. How do you simplify fractions?

**Tip:** Always check if a fraction can be simplified further by finding the greatest common divisor (GCD) of the numerator and the denominator.

Learn how to convert the decimal 19.875 to a mixed fraction step-by-step with detailed explanations. This problem covers the conversion of decimals to fractions, including finding the greatest common divisor (GCD) and combining whole numbers with fractions. Suitable for students in Grades 5-7.

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