Question

Which number below will give the sum of zero when added to 1,235? A. 1.235 B. -1.235 C. 2.470 D. -2.470 For questions \(8-13\), write your answers in the blanks.

Short answer

The correct answer is B. -1.235.

Step-by-step solution

Understand the problem

You need to find a number that, when added to 1,235, results in zero.

Set up the equation

Let the unknown number be represented by x. The equation can be written as: 1,235 + x = 0

Solve the equation

To find x, subtract 1,235 from both sides of the equation: x = 0 - 1,235 Therefore, x = -1,235

Identify the correct answer

Compare the solution to the given options: A. 1.235 B. -1.235 C. 2.470 D. -2.470 The correct answer is B. -1.235

Key concepts

Basic Algebra

When approaching algebra problems, it's important to understand the basic principles. Algebra helps us solve for unknown values. In our exercise, we needed to find what number added to 1,235 results in zero. This kind of problem is fundamental in algebra. Remember, algebra uses symbols (usually letters) to represent unknown numbers. The equation we used is 1,235 + x = 0. Here, x is our unknown number. Starting from this equation, we apply algebraic rules, like adding or subtracting the same value on both sides, to isolate the variable and find its value.

Solving Equations

To solve an equation means finding the value of the unknown variable that makes the equation true. In our example, we needed to solve the equation 1,235 + x = 0. To do this, we need to isolate the variable x. This can be achieved by performing the opposite operation of what is currently being done to x. Here, x is being added to 1,235. Therefore, we subtract 1,235 from both sides of the equation: 1,235 + x - 1,235 = 0 - 1,235. Simplifying this, we get x = -1,235. This tells us that the number needed to add to 1,235 to make zero is -1,235.

Understanding Integers

Integers are the set of whole numbers and their opposites. This includes ...-3, -2, -1, 0, 1, 2, 3,... and so on. In our exercise, we worked with both positive and negative integers. Specifically, we needed the integer that, when added to 1,235 (a positive integer), results in zero. This number is its negative counterpart, -1,235. When dealing with integers, it's helpful to remember that each number has an opposite (or additive inverse), which is the same number with the opposite sign. When a number and its opposite are added together, they always sum to zero. This concept is crucial in understanding how to balance equations and find solutions in algebra.