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Mixed numbers are numbers that contain both a whole number and a fraction, like \(2 \frac{3}{10}\).
To make the subtraction easier, we first convert these mixed numbers into improper fractions.
An improper fraction has a numerator larger than its denominator.
To convert a mixed number to an improper fraction, use the formula:

• Multiply the whole number by the denominator.
• Add the numerator to this product.
• Place the result over the original denominator.

For example, let's convert \(2 \frac{3}{10}\):
1. Multiply the whole number by the denominator: \(2 \times 10 = 20\)
2. Add the numerator: \(20 + 3 = 23\)
3. Place this over the original denominator: \( \frac{23}{10}\)
Similarly, for \(1 \frac{9}{10}\):
1. Multiply the whole number by the denominator: \(1 \times 10 = 10\)
2. Add the numerator: \(10 + 9 = 19\)
3. Resulting in: \( \frac{19}{10}\)

After performing the subtraction operation with improper fractions, we often get a fraction that can be simplified.
Simplifying a fraction means reducing it to its simplest form where the numerator and the denominator cannot be divided by any number other than 1.
To simplify a fraction, you need to:

• Find the greatest common divisor (GCD) of the numerator and the denominator.
• Divide both the numerator and the denominator by the GCD.

Let's simplify \( \frac{4}{10} \):
1. The numerator is 4, and the denominator is 10.
2. Find the GCD of 4 and 10, which is 2.
3. Divide both by 2: \( \frac{4 \div 2}{10 \div 2} = \frac{2}{5} \)
The fraction \( \frac{4}{10} \) simplifies to \( \frac{2}{5} \).
This process makes fractions easier to work with and understand.

Solving math problems step-by-step is crucial for understanding and accuracy.
This structured approach helps you keep track of operations and reduces the chance of errors.
Here's how to tackle subtracting mixed numbers step-by-step:

1. **Convert Mixed Numbers to Improper Fractions**:
First, convert the mixed numbers to improper fractions as we did for \(2 \frac{3}{10}\) and \(1 \frac{9}{10}\). This gives us \( \frac{23}{10} \) and \( \frac{19}{10} \).

2. **Subtract the Improper Fractions**:
Since both fractions have the same denominator, subtract the numerators directly:
\( \frac{23}{10} - \frac{19}{10} = \frac{4}{10} \).

3. **Simplify the Fraction**:
Finally, simplify the resulting fraction \( \frac{4}{10} \) by dividing the numerator and the denominator by their GCD (which is 2).
This results in \( \frac{2}{5} \).

By following these steps methodically, you can solve similar problems with ease and develop a strong foundation in math.