Problem 50 - Algebra A Combined Function

Question

Simplify. See Sections 1.5 and \(1.6 .\) \(\frac{2-2}{3-5}\)

Step-by-Step Solution

Answer

The simplified result is 0.

Step 1: Simplify the Expression in the Numerator

The expression in the numerator is \(2 - 2\). Calculate the result by subtracting 2 from 2.\[2 - 2 = 0\]The numerator simplifies to 0.

Step 2: Simplify the Expression in the Denominator

The expression in the denominator is \(3 - 5\). Calculate the result by subtracting 5 from 3.\[3 - 5 = -2\]The denominator simplifies to -2.

Step 3: Divide the Simplified Numerator by the Simplified Denominator

Now, substitute the simplified values into the original fraction:\[\frac{0}{-2}\]Since any number divided by zero is zero, the fraction simplifies to 0.

Key Concepts

Numerator and Denominator

Fractions are made up of two main parts: the numerator and the denominator. The numerator is the top number, and it tells us how many parts of a whole we have. The denominator is the bottom number and shows how many equal parts the whole is divided into. For example, in the fraction \(\frac{3}{4}\), 3 is the numerator, and 4 is the denominator.

In the fraction from the original exercise, \(\frac{2-2}{3-5}\), the expression "\(2 - 2\)" is the numerator and "\(3 - 5\)" is the denominator.

Understanding how these parts work helps simplify fractions and solve math problems efficiently. Always simplify the numerator and the denominator individually first before applying other operations.

Subtraction of Integers

Subtraction of integers is all about finding the difference between two numbers. Knowing the basic rules of subtracting integers helps prevent errors.

Here are some key points:

• Subtracting a smaller number from a larger number results in a positive number.
• Subtracting a larger number from a smaller number results in a negative number.
• Subtracting any number from itself gives zero.

For example, in the numerator of \(2 - 2\), the result is 0 because the numbers are the same.
In the denominator \(3 - 5\), you're subtracting a larger number (5) from a smaller number (3), resulting in \(-2\). These rules play a critical role in correctly simplifying expressions.

Division with Zero

Division with zero can be quite tricky. Understanding the rules about zero in division is essential for simplifying expressions and avoiding mistakes.

Here are the rules:

• A non-zero numerator divided by zero results in an undefined expression that is not allowed in mathematics.
• A zero numerator divided by any non-zero number results in zero.
• Dividing zero by zero results in an undefined form, as it raises mathematical inconsistencies.

In our exercise, when we have \(\frac{0}{-2}\), the numerator is zero and the denominator is \(-2\).
This means the fraction simplifies beautifully to 0, an excellent and straightforward result when understanding division involving zero.