Adding a Number to -1/3 2/3 to Get 3/4: A Step-by-Step Guide

Solving mathematical problems is a fundamental skill, especially when working with fractions. This article will guide you through the process of adding a number to -1/3 2/3 to obtain 3/4. We'll break down the problem into simple steps and explain each part in detail. By the end, you will have a clear understanding of how to solve similar problems using algebraic operations and basic arithmetic.

Understanding the Problem

We want to find an unknown value (x) that, when added to the sum of -1/3 and 2/3, results in 3/4. Mathematically, we can represent this as:

-1/3 2/3 x 3/4

Step-by-Step Solution

To solve for x, follow these steps:

First, simplify -1/3 2/3:

-1/3   2/3  1/3

The equation now becomes:

1/3   x  3/4

To isolate x, subtract 1/3 from both sides of the equation:

x  3/4 - 1/3

Convert 3/4 and 1/3 to a common denominator (12) to subtract them:

x  (9/12) - (4/12)  5/12

Thus, the value of x is:

x  5/12

Verification

To verify our solution, let's add 5/12 to -1/3 2/3:

-1/3   2/3   5/12

Simplify -1/3 2/3: 1/3 2/3 1/3 Add 5/12 to 1/3:

1/3   5/12

Convert 1/3 to 4/12 to add the fractions:

4/12   5/12  9/12  3/4

The result is 3/4, confirming that adding 5/12 to -1/3 2/3 indeed gives us 3/4.

Conclusion

Adding a number to -1/3 2/3 to obtain 3/4 involves a series of algebraic operations and basic arithmetic. By carefully following each step, you can solve similar problems with ease. Remember to simplify fractions, convert to a common denominator, and isolate the variable to find the solution.