Problem 45 - Basic College Mathematics

Question

Simplify. $$ \frac{8-1}{9-8} $$

Step-by-Step Solution

Answer

7

Step 1: Identify Numerator and Denominator

The expression to simplify is \( \frac{8-1}{9-8} \). Here, the numerator is \( 8-1 \) and the denominator is \( 9-8 \).

Step 2: Simplify the Numerator

Calculate the value of the numerator: \( 8-1 \). This simplifies to \( 7 \).

Step 3: Simplify the Denominator

Calculate the value of the denominator: \( 9-8 \). This simplifies to \( 1 \).

Step 4: Divide the Simplified Numerator by the Simplified Denominator

Now, divide the simplified numerator by the simplified denominator: \( \frac{7}{1} \). This simplifies to \( 7 \).

Key Concepts

Numerator

Let's begin by understanding what a numerator is. The numerator is the top part of a fraction. It represents how many parts of a whole are being considered. In the fraction \( \frac{8-1}{9-8} \), the numerator is \( 8-1 \).
When you simplify the numerator \( 8 - 1 \), you subtract 1 from 8 to get 7. This means our new numerator is 7.
In general, always simplify the numerator by performing any arithmetic operations present.

Denominator

Next, let's look at the denominator. The denominator is the bottom part of a fraction. It tells you how many equal parts the whole is divided into. In the given fraction \( \frac{8-1}{9-8} \), the denominator is \( 9-8 \).
When you simplify the denominator \( 9 - 8 \), you subtract 8 from 9 to get 1. This means our new denominator is 1.
Like with the numerator, always simplify the denominator by performing any arithmetic operations.

Division

Finally, let’s tackle division in the context of fractions. Division in fractions involves dividing the numerator by the denominator.
After simplifying our numerator to 7 and our denominator to 1, we simply perform the division: \( \frac{7}{1} = 7 \).
In simpler terms, dividing any number by 1 keeps the number unchanged. Hence, \( \frac{7}{1} = 7 \). This is why the simplified form of the original fraction \( \frac{8-1}{9-8} \) is 7.