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Chapter 1: Problem 67

Evaluate:\(7-(3 \times 2)\)

Short Answer

Expert verified
The result of the expression is 1.

Step by step solution

01

Perform Multiplication Inside the Parentheses

Start by evaluating the expression inside the parentheses. Multiply 3 by 2 to find the product. \(3 \times 2 = 6\)
02

Substitute the Result in the Expression

Replace the expression inside the parentheses with the result from Step 1. The expression now becomes:\(7 - 6\)
03

Subtract to Find the Final Result

Perform the subtraction operation by subtracting 6 from 7. \(7 - 6 = 1\)

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Key Concepts

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

Parentheses
Parentheses are an essential element in mathematics for grouping parts of an expression. When you see parentheses in a mathematical expression, it indicates which operations should be performed first. This can change the outcome of a calculation considerably.

In our example, the expression is \(7-(3 \times 2)\). The part inside the parentheses, \(3 \times 2\), tells us that multiplication should be evaluated before the subtraction. By solving what's inside the parentheses first, we maintain the correct order of operations.

  • Always look for parentheses first in any expression
  • Complete all operations inside the parentheses before moving to step outside
  • Double-check your work by solving the parentheses portion independently to avoid mistakes

This clarity ensures that everyone computes the expression in a consistent manner, promoting accuracy in problem-solving.
Multiplication
Multiplication within expressions acts as one of the higher-priority operations when considering the order of operations. In expressions with multiple operations, multiplication is generally performed after parentheses but before addition and subtraction.

  • In the problem \(7-(3 \times 2)\)
  • The multiplication \(3 \times 2 = 6\) is performed first
  • This step simplifies the expression to \(7 - 6\)

This emphasizes how multiplication needs attention first, just after solving any parentheses. This order ensures that expressions are handled correctly and consistently, resulting in the outcome that mathematicians intend.
Subtraction
Subtraction is a basic arithmetic operation with lower precedence than both parentheses and multiplication. After resolving expressions inside parentheses and performing any multiplications, subtraction is calculated as a final step.

In our specific exercise, once we simplified the initial expression to \(7 - 6\) after solving inside the parentheses and multiplication, we proceed with subtraction.

  • 7 represents the minuend, which is the number from which another number is to be subtracted.
  • 6 is the subtrahend, the number that gets subtracted from the minuend.
  • The final operation \(7 - 6\) evaluates to 1

Completing the operation successfully provides the final result, illustrating how subtraction concludes the sequence of order of operations in this example.

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Most popular questions from this chapter

Calculate and express each result in its simplest form:\(\left(-\frac{2}{3}\right) \times\left(-\frac{3}{4}\right)\)

Calculate and express each result in its simplest form:\(\frac{11}{12}+\frac{3}{16}\)

Find the sum and product of the pairs of complex numbers:\(z_{1}=1-6 i, z_{2}=-5-4 i\)

Evaluate:\((7+3) \times 4-5\)

Calculate and express each result in its simplest form:\(\frac{2}{15} \div \frac{4}{5}\)
See all solutions

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