Problem 60 - Prealgebra and Introductory Algebra

Question

Write the expression in words. $$6-(-7)$$

Step-by-Step Solution

Answer

The expression 6 minus negative 7 in words is 'six plus seven'.

Step 1: Understand the expression

Firstly, examine the expression. It's showing 6 minus negative 7. In mathematics, subtracting a negative number is the same as adding a positive version of that number.

Step 2: Rewrite the expression

Knowing the rules of subtracting negative numbers, the expression can be rewritten as 6 plus 7.

Step 3: Write the expression in words

Finally, the numerical expression will be translated into English. Therefore, 6 plus 7 becomes 'six plus seven'.

Key Concepts

Numerical Expression in Words

When dealing with mathematics, being able to translate a numerical expression into words enhances understanding and communication, especially in an educational setting. It's a way to express the calculations verbally. In our exercise, we have the expression \(6 - (-7)\), which, when put into words, is 'six minus negative seven.'

However, this expression can be simplified as well. In the world of integers, subtracting a negative is akin to adding its positive counterpart. Therefore, this expression is equivalent to saying 'six plus seven.' Even though this seems like a basic step, accurately translating numerical expressions into words is indispensable for students as they begin to tackle more complex mathematical problems. It also helps in verifying the understanding of the operations involved.

Addition of Integers

Understanding the addition of integers is fundamental in mathematics. Integers include all whole numbers and their negatives, not forgetting zero as well. In the context of our exercise, we have two integers: 6 and -7.

The operation we're presented with is subtraction, but it's important to recognize that when we subtract a negative number, it becomes addition. This concept is crucial as it lays the groundwork for solving a wide range of mathematical problems. To reinforce this idea, think of subtraction as removing or taking away, and when you 'take away' a debt (negative), you're essentially 'adding' to your wealth (positives). Therefore, \(6 - (-7)\) is transformed into the addition of integers: \(6 + 7\). This simplification removes any confusion and aids in completing the operation swiftly and accurately.

Basic Algebra

At the heart of understanding mathematical expressions and equations lies a fundamental grasp of basic algebra. This area of mathematics provides the tools for describing and solving problems with unknowns and variables, but it also informs how we manipulate numerical expressions.

In our exercise, we aren't dealing with unknowns. However, we are applying an algebraic rule that says 'subtracting a negative number is the same as adding a positive one.' This is an elementary concept within algebra that often perplexes beginners. The switch from subtraction to addition is an example of the underlying principles of algebra where operations can transform to make calculations easier. As students progress, they'll encounter equations where this rule becomes an essential step in finding solutions. Therefore, understanding the simple rearrangement of \(6 - (-7)\) to \(6 + 7\) is a stepping stone in the mastery of algebra.