Problem 85 - Prealgebra and Introductory Algebra

Question

Subtract. $$3-(-4)$$

Step-by-Step Solution

Answer

The answer to the problem \(3-(-4)\) is 7. So, when you subtract a negative number from a positive number, it is equivalent to adding the absolute value (positive value) of the negative number to the positive number.

Step 1: Identifying the problem

We have been given a subtraction problem where a negative number is to be subtracted from a positive number. The problem is \(3-(-4)\), which can also be written as \(3-(-4)\). The aim is to simplify this expression.

Step 2: Apply the Mathematical Rule

According to the rules of mathematics, the minus sign preceding the negative number in the expression is treated as if it is adding a positive number. Hence, the given expression \(3-(-4)\) can be rewritten as \(3+4\).

Step 3: Simplify the Expression

Now simplify the expression by adding numbers together. The result when 3 is added to 4 will be the answer to the exercise.

Key Concepts

mathematical rules

Understanding mathematical rules is essential when performing operations with numbers. These rules serve as guidelines that ensure the operations we perform maintain consistency and correctness. In subtraction, when faced with subtracting a negative number, one crucial rule to remember is the "double negative" rule.

When a negative sign appears in front of a negative number, this combination can be transformed to addition. For instance, in the expression \(3 - (-4)\), the subtraction sign immediately followed by a negative number signifies that you should add. Hence, \(3 - (-4)\) becomes \(3 + 4\). Understanding and applying such rules allows you to simplify problems accurately.

simplification

Simplification in mathematics involves transforming an expression to its simplest form, making it easier to understand and solve. When you simplify expressions, you're essentially reducing them to their most basic form without changing their value.

In the expression \(3 - (-4)\), simplification involves applying the rule about negatives to change it to an addition problem. Here, the expression turns into \(3 + 4\). This step eliminates extra characters (like double negatives) and results in a straightforward task. Finally, you solve the simpler expression, which in this case, yields a sum of 7. Simplification assists in problem-solving by clarifying what needs to be calculated.

negative numbers

Negative numbers are essential components of mathematics, designed to represent values below zero on the number line, in opposition to positive numbers. Understanding how to work with them, especially in the context of operations like subtraction, is crucial.

When you subtract a negative number, you're essentially performing an operation akin to addition. This is because a double negative (subtracting negative) turns into a positive. For example, \(3 - (-4)\) becomes \(3 + 4\), as you're actually "adding" 4 to 3. This demonstrates how negative numbers behave in arithmetic operations. Always remember: removing a negative is like gaining a positive, thus flipping the operation sign.

expressions

Mathematical expressions are combinations of numbers, symbols, and operators (like +, -, ×, ÷) that define a particular value. Expressions are evaluated following specific operations and rules.

Consider the expression \(3 - (-4)\). This expression might initially look complex due to the use of a negative number in subtraction. However, by rewriting it as \(3 + 4\), it becomes simpler to evaluate. Understanding how to manipulate and transform expressions is vital in mathematics,

as it allows you to solve them accurately and efficiently. Practice with expressions enhances your problem-solving skills, enabling you to deal with increasingly complex mathematical challenges.