Problem 5 - Fundamentals of Mathematics

Question

Write each expression in words. \(-1-(-8)\)

Step-by-Step Solution

Answer

Negative one plus eight.

Step 1: Identify the Expression

The given expression is \(-1 - (-8)\)\.

Step 2: Rewrite Negative Signs

Understand that subtracting a negative number is the same as adding its positive counterpart. So, the expression \(-1 - (-8)\)\ can be rewritten as \(-1 + 8\)\.

Step 3: Convert Mathematical Symbols to Words

Expression \(-1 + 8\)\ in words is 'negative one plus eight.'

Key Concepts

Negative Numbers

Negative numbers are figures that represent a value less than zero. If you think about temperatures, negative numbers are used to express degrees below freezing. They are crucial in daily life for representing debts, temperature below zero, or other values that decrease below a starting point.

When you see a number with a minus sign like \(-1\), it simply means one less than zero, or a move one unit away from positive numbers. It's essential to understand negative numbers to effectively manage situations involving low balances, reverse direction, or cooling down."},{

Subtracting Negatives

At first glance, subtracting a negative number can seem tricky. However, it's easier than it looks. Subtracting a negative number is the same as adding a positive number. Imagine that the 'double negative' rule transforms a complex-looking subtraction into a simple addition.

For example, when you encounter an expression like \(-1 - (-8)\), think about it this way: subtracting \(-8\) is equivalent to adding \(8\) instead. In essence, you are increasing the value by \(8\) instead of decreasing or deducting it. So, the expression \(-1 - (-8)\) becomes \(-1 + 8\), which is far easier to compute.

Mathematical Symbols to Words

Using words to express mathematical symbols can make problems easier to solve by clarifying what the numbers and operations signify. Converting \(-1 + 8\) into words involves articulating each component:

• \(-1\) becomes 'negative one,' signaling a starting point below zero.
• The plus sign \(+\), corresponds to the word 'plus,' indicating an addition operation.
• Finally, \(8\) remains 'eight,' the number being added.

Thus, the equation \(-1 + 8\) is read as 'negative one plus eight,' making it intuitive and more understandable. By verbally mapping out math symbols, you break down the complexity and simplify both solving and interpreting mathematical expressions.