Problem 93 - Prealgebra

Question

Simplify the given expression. \(\frac{-18.22-6.7}{14.75-7.75}\)

Step-by-Step Solution

Answer

The simplified expression is \(-3.56\).

Step 1: Identify the Numerator and Denominator

In the given expression \( \frac{-18.22 - 6.7}{14.75 - 7.75} \), the numerator is \(-18.22 - 6.7\) and the denominator is \(14.75 - 7.75\).

Step 2: Calculate the Numerator

To simplify the numerator, perform the subtraction \(-18.22 - 6.7\). This yields \(-18.22 - 6.7 = -24.92\).

Step 3: Calculate the Denominator

To simplify the denominator, perform the subtraction \(14.75 - 7.75\). This results in \(14.75 - 7.75 = 7.0\).

Step 4: Form the New Expression

After calculating the numerator and denominator, we form the new fraction: \( \frac{-24.92}{7.0} \).

Step 5: Divide the Numerator by the Denominator

Finally, divide the simplified numerator by the simplified denominator: \(-24.92 \div 7.0 = -3.56\). This is the simplified form of the original expression.

Key Concepts

Understanding Numerators and Denominators

A fraction consists of two main parts: the numerator and the denominator. Understanding these components is crucial for simplifying expressions. The numerator is the top part of the fraction, showing how many parts we have. For example, in our expression, the numerator is

• -18.22 - 6.7

This tells us that we need to perform the subtraction in this part.
On the other hand, the denominator is the bottom part, representing the total number of equal parts in a whole or in this case,

• 14.75 - 7.75

Understanding this will help us know what calculation we'll be working on to transform the fraction into something easier to manage. Whenever dealing with fractions, make sure to separate and handle the numerator and the denominator separately before combining their simplified forms.

Easy Navigation of Subtraction

Subtraction is an operation that takes one number away from another. In the context of simplifying expressions, you often need to subtract values both in the numerator and the denominator to simplify a fraction. When handling our given expression, we simplify the numerator by performing the subtraction:

• -18.22 minus 6.7 gives us -24.92

Next, we perform subtraction on the denominator:

• 14.75 minus 7.75 equals 7.0

Subtraction can sometimes be tricky when working with negative numbers.
Remember, subtracting a negative can change the sign or the overall result, so always double-check your signs to ensure accuracy.
Properly executing these subtraction steps is key in successfully simplifying the expression before proceeding to division.

The Role of Division in Simplifying Expressions

Division is the action of splitting a number into specified equal parts. Once we have simplified the numerator and denominator through subtraction, the next step is to divide the simplified numerator by the simplified denominator. In our expression after simplifying, we have:

• Nominator: -24.92
• Denominator: 7.0

To find the simplified value of the fraction, perform the division:

• -24.92 divided by 7.0 equals -3.56

This step is straightforward, yet it often seals the deal for simplifying the complete expression.
Remember, dividing a negative by a positive will result in a negative outcome, as shown in our solution. Mastering each division step is essential for arriving at the correct simplified expression effortlessly. By focusing on accurate division, you'll efficiently uncover the most simplified form of any fraction in your exercises.