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Chapter 6: Problem 42

Simplify. $$ 2 \cdot 7-(5+1) $$

Short Answer

Expert verified
8

Step by step solution

01

Evaluate the Multiplication

First, evaluate the multiplication part of the expression: \(2 \times 7\). This gives us: \[2 \times 7 = 14\].
02

Evaluate the Expression Inside the Parentheses

Next, simplify the expression inside the parentheses: \(5 + 1\). This gives us: \[5 + 1 = 6\].
03

Substitute Back into the Expression

Now, substitute the values back into the original expression: \(14 - 6\).
04

Perform the Subtraction

Finally, perform the subtraction: \[14 - 6 = 8\].

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Key Concepts

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

order of operations
When simplifying mathematical expressions, it's essential to follow the order of operations. This rule dictates the sequence in which different operations should be carried out to avoid confusion and ensure consistency. The standard order is:
  • Parentheses (or brackets)
  • Exponents (or powers)
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) can help you remember this order. Ignoring the order of operations can lead to incorrect results, which is why it's crucial to adhere to these rules.
multiplication
In the expression, the first operation we need to perform is multiplication:

The original expression is: ewline \[2 \times 7 - (5 + 1) \]

According to the order of operations, we need to complete the multiplication first: ewline \[2 \times 7 = 14 \]
Now our expression looks like this: ewline \[14 - (5 + 1)\]
Always remember that multiplication must be done before any addition or subtraction unless specified by parentheses.
parentheses
After handling multiplication, we move on to expressions within parentheses:

Our modified expression is: ewline \[14 - (5 + 1) \]
Inside the parentheses, we have: ewline \[5 + 1 \] which simplifies to 6.
Now, substitute this back into the expression: ewline \[14 - 6\]
Parentheses help group parts of an expression and ensure specific operations are carried out first, so always evaluate them before moving on.
subtraction
Finally, we perform the subtraction:

With our simplified expression now being: ewline \[14 - 6 \]
Subtraction is done last according to the order of operations: ewline \[14 - 6 = 8\]
This final step gives us the simplified result, which in this case is 8.
Remember, when handling subtraction, always ensure that all previous operations (like parentheses and multiplication) have been completed.

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