Question

Simplify the expression.\((4-7)(-2)\)

Short answer

The simplified expression is 6.

Step-by-step solution

Perform the operation inside the brackets

Following the order of operations, BIDMAS, first simplify the expression inside the brackets \(4 - 7\). This gives the value of \(4 - 7 = -3\). Now the expression is \(-3 * -2\).

Multiply the values

In the second step, multiply the result that you got from step 1 by \( -2 \). Calculating \(-3 * -2\) gives \( 6 \).

Key concepts

Order of Operations

The Order of Operations is a fundamental principle in algebra that dictates the proper sequence in which mathematical operations should be performed to ensure consistency and accuracy. This principle is often remembered by the acronym BIDMAS, which stands for Brackets, Indices, Division and Multiplication, and Addition and Subtraction.

• Brackets: Always solve expressions within brackets first.
• Indices: Then, solve powers or roots in the expression.
• Division and Multiplication: These operations take the next level of priority, and are solved from left to right.
• Addition and Subtraction: Lastly, perform these, also from left to right.

In the given exercise, we begin with what's inside the brackets: \(4 - 7\). Solving this ensures that you are following the correct order, leading to accurate results in further calculations. For any mathematical expression, always remember to identify any operations within brackets first, as demonstrated in this example.

Negative Numbers

Negative numbers represent values that are less than zero and play a crucial role in math, especially in algebraic simplification. Understanding how to handle negative numbers is key to simplifying expressions like \((4-7)(-2)\).

Negative numbers have unique rules:

• Adding a negative number is equivalent to subtraction: \(5 + (-3)\) is the same as \(5 - 3\).
• Subtracting a negative number results in addition: \(5 - (-3)\) becomes \(5 + 3\).

In the provided expression, simplifying \(4-7\) effectively is about understanding that subtracting a larger number from a smaller number yields a negative result: \(-3\). Recognizing how negative numbers behave helps in avoiding common mistakes, especially in longer equations full of operations like this.

Multiplication of Integers

Multiplication of integers involves rules that are straightforward but crucial for anyone dealing with algebraic expressions, especially when negative integers are involved.

Here are the basic rules:

• Positive times positive gives a positive: \((+3) \times (+2) = +6\).
• Negative times positive yields a negative: \((-3) \times (+2) = -6\).
• Positive times negative gives a negative: \((+3) \times (-2) = -6\).
• Negative times negative results in a positive: \((-3) \times (-2) = +6\).

In the example -3 \times -2\, the multiplication of two negative numbers resulting in a positive value \(+6\) demonstrates an important principle. Ensuring you understand these rules ensures accuracy when simplifying expressions involving multiplication.