Problem 61 - Prealgebra and Introductory Algebra

Question

Write the expression in words. $$-14-(-3)$$

Step-by-Step Solution

Answer

The written expression for '-14-(-3)' is 'Negative fourteen plus three'.

Step 1: Understand the expression

The expression given is '-14-(-3)'. Notice that the second term is a negative of negative three, which according to the rules of mathematics, simplifies to positive three.

Step 2: Convert the expression into addition

The expression '-14-(-3)' simplifies to '-14+3' because in mathematics two negatives make a positive.

Step 3: Write the expression in words

After understanding the expression and converting it into addition, the written expression of '-14-(-3)' is 'Negative fourteen plus three'.

Key Concepts

Integer Operations

Integer operations form the basis for many mathematical calculations. They involve dealing with whole numbers, which can include positive numbers, negative numbers, and zero. Understanding integer operations is crucial for simplifying and manipulating expressions.

One important operation is subtraction, and when dealing with negative integers, it can often appear tricky. The general rule is that subtracting a negative number is the same as adding its positive counterpart. For example:

• The expression \(-(-3)\) first asks us to subtract negative three.
• According to mathematical rules, this simplifies to adding positive three.

This concept is crucial when simplifying complex expressions and understanding integer behaviors. Mastering this rule will greatly enhance your ability to handle different mathematical problems and expressions.

Mathematical Expressions in Words

Expressing mathematical expressions in words is a great way to deepen your understanding of the concepts behind the numbers. It involves translating numeric expressions into verbal statements.

In our original exercise, we are tasked with writing the expression \(-14 - (-3)\) in words. To do this, first simplify the expression based on integer operation rules. We understand that \(-14 - (-3)\) simplifies to \(-14 + 3\). Now, focus on expressing this simplified phrase.

Once simplified, we can now write the expression as \'Negative fourteen plus three\'. This phrasing allows us to clearly understand and convey the expression's numerical intent through language, making it more relatable and comprehensible.

Simplifying Expressions

Simplifying expressions is a key skill in mathematics that helps to make complex problems more manageable. It often involves reducing an expression to its simplest form by performing operations and applying algebraic rules.

To simplify expressions involving negative numbers, focus on simplifying the terms using known rules, such as turning two negatives into a positive. In our expression \(-14 - (-3)\), this principle was applied:

• The negative of negative three \((-(-3))\) was converted to positive three.
• This turned the equation into \(-14 + 3\).

Continuous practice with simplifying expressions will improve problem-solving skills, making mathematical operations like these feel intuitive over time. By breaking down each part of an equation and applying the right rules, you can always reach a more straightforward or manageable form.