Problem 84 - Algebra 1

Question

Evaluate the expression. \(-\frac{1}{3}+6+\frac{1}{3}\)

Step-by-Step Solution

Answer

The expression evaluates to \(6\).

Step 1: Identify the problem

The problem requires the evaluation of the expression: \(-\frac{1}{3}+6+\frac{1}{3}\).

Step 2: Begin with the fraction subtraction

Start by subtracting \(-\frac{1}{3}\) from \(\frac{1}{3}\). This results in \(0\). This is because subtracting a negative negates the subtraction action and effectively adds a positive \(\frac{1}{3}\) to the existing \(\frac{1}{3}\), which results in \(\frac{2}{3}\). And, \(\frac{2}{3} - \frac{2}{3}\) equals \(0\).

Step 3: Add the integer

Next, add the integer \(6\) to the result of the fraction subtraction in the previous step, which is \(0\). This gives us \(6\).

Key Concepts

Fraction Subtraction

When tackling fraction subtraction, the process can feel tricky at first. Start by identifying the fractions involved. In this exercise, we have:

• \( -\frac{1}{3} \)
• \( \frac{1}{3} \)

The rule of subtracting fractions, especially when dealing with negative numbers, can be simplified by understanding that subtracting a negative fraction is equivalent to adding its positive counterpart. For example, \(-\frac{1}{3}\) subtracted from \(\frac{1}{3}\) is like adding \(\frac{1}{3}\), resulting in \(\frac{2}{3}\). However, in our original problem, we understand that the entire fraction part sums to zero. By focusing on logic and understanding signs, you'll master fraction subtraction in no time!
Work slowly at first and double-check your steps. Mistakes often happen when rushing through calculations. Always remember that fractions with a negative sign are trickier but not impossible.

Negative Numbers

Negative numbers can initially be a bit baffling, but they follow clear rules that help in computations. Dealing with negative values such as \(-\frac{1}{3}\) requires an understanding of arithmetic involving negatives. Here are some basic points to remember:

• Subtracting a negative number is the same as adding its positive. For instance, subtracting \(-\frac{1}{3}\) from a number is like adding \(\frac{1}{3}\).
• Negative numbers are below zero on the number line and opposite to positive numbers in value and direction.

Understanding these properties makes computations easier, such as in our exercise where combining negatives effectively simplifies the fractions to zero.

Integer Addition

Integer addition is one of the basic and probably the simplest arithmetic operations you will encounter. It's important not to be intimidated by the mix of fractions and integers, as seen in this example. The main operation in this problem comes after simplifying the fractional parts.
The number 6 is our integer in the expression. Once fractional subtraction results in zero, adding this integer is straightforward:

• Simply place 6 and add any number, which in this case is zero.
• Mathematically, it is written as \(0 + 6 = 6\).

The key to understanding integer addition lies in grasping that it's about summing whole numbers, regardless of whether the added number comes after dealing with fractions or not. Stay confident in your calculations, practice often, and soon addition will become second nature!