Problem 28 - Fundamentals of Mathematics

Question

For the following 6 problems, write each expression in words. $$ -7-(-2) $$

Step-by-Step Solution

Answer

Negative seven minus negative two.

Step 1: Understand the Expression

We are given the mathematical expression \(-7 - (-2)\). This expression consists of a negative seven and the subtraction of negative two.

Step 2: Identify the Components

The expression consists of three key mathematical components: a negative number, subtraction, and another negative number, specifically \(-7\) and \(-2\).

Step 3: Translate into Words

The expression \(-7 - (-2)\) can be translated into words by stating it sequentially: "Negative seven minus negative two."

Key Concepts

Negative Numbers

Negative numbers are an essential part of understanding mathematics as they extend the number line to include values less than zero. When we work with negative numbers, we're dealing with values that signify absence or deficit, such as a debt or a temperature below freezing points. In mathematical notation, a negative number is represented by a minus "-" sign placed before a number.

• Understanding: Negative numbers like \(-7\) indicate a value 7 units less than zero.
• Comparison with Positive Numbers: They are less than zero and less than all positive numbers, which increases as they move further left on the number line.

In the expression \(-7 - (-2)\), both -7 and -2 are negative numbers, representing situations where values are being removed or subtracted from each other, resulting in directions or calculations that pull back from the standard positive counting numbers we often use.

Subtraction

Subtraction is a basic operation in arithmetic that involves finding the difference between numbers. This operation is often represented with the "-" (minus) symbol and is foundational for solving problems that involve removing quantities or finding out how much more one item is compared to another.

• Basic Idea: In simple terms, subtraction answers the question "What remains?" or "How many less?" For example, subtraction tells us the remaining apples if we take away some from a bunch.
• When Negative Numbers are Involved: In expressions like \(-7 - (-2)\), the subtraction of a negative is tricky. The subtraction of a negative number is equivalent to the addition of a positive number. This is because removing debt is like gaining credit.

Therefore, \(-7 - (-2)\) effectively results in adding 2 to -7, leading to \(-7 + 2\), resulting in \(-5\). The operation explains how subtraction can expand into more complex number interactions, especially involving negative numbers.

Translation into Words

Expressing mathematical expressions in words helps bridge the gap between symbolic mathematics and verbal understanding. Translating \(-7 - (-2)\) into words enhances comprehension and clarity, essential for educational environments and everyday comprehension.

• Step-by-Step Translation: Begin by identifying each part of the expression. \(-7\) reads as "negative seven," and \(-\) reads as "minus," while \(-2\) reads as "negative two." Thus, the full expression becomes "Negative seven minus negative two."
• Importance for Learning: Putting equations into words aids learners in grasping more than just the mechanics of math but also its narrative. It turns the abstract into something relatable.

Just as reading a story can reveal nuances, so can articulating math problems in words unveil deeper understanding, grounding math in language and logic.