Problem 91 - Prealgebra

Question

Simplify the given expression. \(\frac{17.76-(-11.7)}{0.52}\)

Step-by-Step Solution

Answer

The simplified expression is 56.65.

Step 1: Understand the Expression

The expression given is \( \frac{17.76 - (-11.7)}{0.52} \). It involves a subtraction in the numerator and a division.

Step 2: Remove Double Negatives

In the numerator, we have \( 17.76 - (-11.7) \). Remember that subtracting a negative number is the same as adding its positive value. Therefore, \( 17.76 - (-11.7) \) becomes \( 17.76 + 11.7 \).

Step 3: Simplify the Numerator

Add the two numbers we have from the previous step: \( 17.76 + 11.7 = 29.46 \). Now the expression is \( \frac{29.46}{0.52} \).

Step 4: Perform the Division

Now divide the numerator by the denominator: \( 29.46 \div 0.52 \). This calculation results in \( 56.65 \).

Step 5: Write the Final Answer

The simplified expression is \( 56.65 \).

Key Concepts

Removing Double Negatives

When working with algebraic expressions, removing double negatives is a fundamental skill. It might sound confusing at first, but it's quite straightforward. In mathematics, subtracting a negative number is the same as adding its positive counterpart. Imagine there's a negative sign to the left of another negative number. This creates a situation often referred to as "double negatives." For example, in the exercise, you have \(17.76 - (-11.7)\). Think of it like this:

• Subtracting \(-11.7\) is identical to adding \(+11.7\).
• So, \(17.76 - (-11.7)\) becomes \(17.76 + 11.7\).

This simple switch can prevent errors in calculations and make your math journey smoother. Always remember: two negatives transform into a positive!

Performing Division in Algebra

Division in algebra isn't too different from regular arithmetic division, but understanding the process is crucial. In algebraic contexts, expressions often involve fractions and variables. However, in our specific exercise, we have numerical values: \( \frac{29.46}{0.52} \). Here's a step-by-step on how to tackle it:

• Divide the numerator (top number) by the denominator (bottom number).
• In our case, divide \(29.46\) by \(0.52\).
• You can do this manually or use a calculator to ensure precision.
• The result simplifies to \(56.65\).

Whether dealing with simple numbers or complex algebraic fractions, grasping the basics of division will enhance your problem-solving skills significantly.

Understanding Algebraic Numerators

A critical part of mastering algebraic expressions is understanding the numerator. The numerator is the top part of a fraction and often requires simplification before any division can occur. In the given exercise, our numerator was initially \(17.76 - (-11.7)\).

• Begin by simplifying within the numerator. This meant removing the double negative: \(17.76 + 11.7\).
• Once simplified, the numerator became \(29.46\).
• Ensuring accuracy in the numerator step-by-step makes the overall problem easier to solve.

By effectively managing the numerator, you ensure that subsequent operations, like division, happen smoothly. Always double-check your work here to avoid any errors in the final result.