Problem 50 - Basic College Mathematics

Question

Simplify. $$ \frac{11-1}{10-9} $$

Step-by-Step Solution

Answer

10

Step 1 - Simplify the numerator

Subtract the numbers in the numerator: \( 11 - 1 \). This gives \( 10 \).

Step 2 - Simplify the denominator

Subtract the numbers in the denominator: \( 10 - 9 \). This gives \( 1 \).

Step 3 - Divide the simplified numerator by the simplified denominator

Divide the result from Step 1 by the result from Step 2: \( \frac{10}{1} = 10 \).

Key Concepts

Numerator

The numerator is the top part of a fraction. It's the number above the line. In the exercise, the numerator is originally expressed as \(11 - 1\). To simplify it:

• Perform the subtraction: \(11 - 1 = 10\).

This means our simplified numerator is 10. Whenever you simplify a fraction, fully resolve any operations in the numerator.

For example, if your numerator was \(12 + 4\), you would add to get \(16\). Always complete these small steps first to make the next steps easier.

Denominator

The denominator is the bottom part of a fraction. It's the number below the line. In this exercise, the denominator is \(10 - 9\). To simplify it:

• Perform the subtraction: \(10 - 9 = 1\).

This simplifies our denominator to 1. Just like the numerator, simplify any operations in the denominator.

For example, if the denominator was \(8 - 3\), you would subtract to get \(5\). Completing this step ensures your fraction is ready for the final calculation.

Division

Division is the process of finding out how many times one number is contained in another. In the context of fractions, you divide the numerator by the denominator. In this exercise, you have:

• Numerator: 10
• Denominator: 1

To simplify the fraction \( \frac{10}{1} \), divide 10 by 1, which equals 10. So, \( \frac{10}{1} = 10 \).

Remember, if your fraction simplifies to have 1 as the denominator, the value of the fraction is simply the numerator. For example, \( \frac{7}{1} = 7 \). Simplifying fractions makes them easier to understand and work with in further calculations.