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Chapter 1: Problem 41

Evaluate each of the following expressions, if possible. $$12-(4 \cdot 3-8)$$

Short Answer

Expert verified
8

Step by step solution

01

Evaluate the expression inside the parentheses

First, solve the expression inside the parentheses: \(4 \times 3 - 8\).
02

Perform the multiplication

Multiply 4 by 3: \(4 \times 3 = 12\)
03

Perform the subtraction

Subtract 8 from 12: \(12 - 8 = 4\)
04

Substitute back and complete the outer subtraction

Replace the inner expression with 4 in the original expression: \(12 - 4\). Then perform the subtraction: \(12 - 4 = 8\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

parentheses in math
In mathematics, parentheses play a crucial role in determining the order in which operations are performed. According to the order of operations, any expression inside parentheses must be evaluated first before dealing with multiplication, division, addition, or subtraction outside them.
For instance, in the expression \(12-(4 \cdot 3-8)\), the part within the parentheses, \(4 \cdot 3 - 8\), must be calculated first. Solving what's inside first prevents mistakes and ensures accuracy.
So, whenever you see parentheses in an expression, always remember to address them first!
multiplication
Multiplication is an essential arithmetic operation that is always tackled before addition and subtraction unless parentheses dictate otherwise. In our example \(12-(4 \cdot 3-8)\), after identifying the expression within the parentheses, you need to perform the multiplication operation within it.
Here, \(4 \cdot 3\) equals 12. By solving this step-by-step, you can ensure clarity in your calculations and avoid mistakes. Multiplication simplifies your numbers, making the next steps easier.
subtraction
Subtraction can be thought of as taking away a number from another. When it comes to evaluating expressions, subtraction is usually tackled last if it appears outside brackets.
In our original example \(12-(4 \cdot 3-8)\), once the multiplication inside the parentheses is handled, the next step is to perform the subtraction within those parentheses: \(12 - 8 = 4\).
Finally, substitute this value back into the outer expression and complete the remaining subtraction: \(12 - 4\).
Thus, applying the steps in the correct order makes solving complex expressions easier and ensures accurate results.

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Most popular questions from this chapter

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$0.24$$

Graph the given set on a number line. \(\\{a | a \text { is a natural number less than } 12 \text { and not divisible by } 3\\}\)

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$4.8$$

Evaluate the given expression. Remember to follow the order of operations. $$48 \div(12 \div 4)$$

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