Problem 95 - Prealgebra

Question

Simplify the given expression. \(\frac{-12.9-(-10.98)}{0.5^{2}}\)

Step-by-Step Solution

Answer

The simplified expression is -7.68.

Step 1: Remove Parentheses

First, address the expression within the numerator, particularly the double negative, which means addition. So, replace \(-(-10.98)\) with \(+10.98\).Now, rewrite the expression as: \(-12.9 + 10.98\).

Step 2: Simplify the Numerator

Perform the arithmetic operation in the numerator: \(-12.9 + 10.98\).Calculate this expression:\(-12.9 + 10.98 = -1.92\).

Step 3: Simplify the Denominator

Next, simplify the denominator. The expression we have is \(0.5^{2}\).Calculate this as follows: \(0.5 \times 0.5 = 0.25\).

Step 4: Divide the Numerator by the Denominator

Now divide the simplified numerator by the simplified denominator:\(-1.92 \div 0.25\).Perform the division:\(-1.92 \div 0.25 = -7.68\).

Key Concepts

Understanding Arithmetic Operations

Arithmetic operations are the basic building blocks in mathematics. They include addition, subtraction, multiplication, and division. Each of these operations allows us to manipulate numbers in various ways to solve problems or simplify expressions.

In our exercise, the main focus was on addition and subtraction within the numerator of the expression. Initially, we see a double negative \(-(-10.98)\), which might seem tricky. But remember, in mathematics, two negatives make a positive. Thus, \(-(-10.98)\) becomes \(+10.98\).

This change helps us to simplify the problem: \(-12.9 + 10.98\). Arithmetic operations are crucial in simplifying such expressions as they directly affect the outcome of the problem. Practice often helps in mastering them.

Simplifying Through Division

Division is a process of distributing a number into an evenly divided group. In the given exercise, division plays a key role in the final steps of simplification.

After simplifying both the numerator \(-1.92\) and the denominator \(0.25\), the expression becomes a straightforward division problem: \(-1.92 ÷ 0.25\).

Performing the division means determining how many times the denominator \(0.25\) fits into the numerator \(-1.92\). This results in the answer \(-7.68\).

Grasping division is vital because many expressions require dividing terms to find a solution. It involves understanding how to break down numbers into smaller, equal parts.

Removing Parentheses in Expressions

Removing parentheses correctly is a skill that can make complex problems much simpler. Parentheses often indicate operations that need resolved first in a math expression.

In our original expression, the parentheses carry a negative symbol. As seen in the step-by-step solution, this involved handling a double negative: \(-(-10.98)\).

Dealing with double negatives used to only rely on two negatives equaling a positive, changing \(-(-10.98)\) into \(+10.98\). Simplifying this way helps to focus on the operations at hand without distractions.

Removing parentheses efficiently makes simplifying expressions straightforward. Always look carefully at what's inside and directly affect the expression around it.