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Chapter 1: Problem 63

Perform each indicated operation. $$ (7-10)(10-4) $$

Short Answer

Expert verified
-18

Step by step solution

01

Perform the subtraction inside the first parenthesis

Subtract 10 from 7 to get the result inside the first parenthesis: \(7 - 10 = -3\)
02

Perform the subtraction inside the second parenthesis

Subtract 4 from 10 to get the result inside the second parenthesis: \(10 - 4 = 6\)
03

Multiply the results from the previous steps

Multiply the results of the two subtractions: \((-3) \times 6 = -18\)

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Key Concepts

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

Subtraction
Subtraction is one of the fundamental operations in arithmetic.
It involves taking one number away from another.
In our exercise, we see two subtractions: Inside the first parenthesis, we have to subtract 10 from 7. This operation is calculated as:
  • \(7 - 10 = -3\)
Notice that since 10 is larger than 7, our answer is a negative number, -3.
In the second parenthesis, we perform another subtraction, 10 minus 4:
  • \(10 - 4 = 6\)
This time, the minuend (10) is larger than the subtrahend (4), giving us a positive result, 6.
It is important to understand these concepts because they form the basis for more advanced algebraic operations.
Parentheses
Parentheses play a crucial role in algebraic operations.
They indicate which operations must be performed first.
In our example, the parentheses tell us to do the subtractions before any other operations.
First, calculate inside the first parenthesis:
  • \(7 - 10 = -3\)
Next, in the second parenthesis:
  • \(10 - 4 = 6\)
Parentheses ensure there is no ambiguity in the operations.
It is essential to handle the operations inside the parentheses correctly to get accurate results for the entire expression.
Multiplication
Multiplication involves combining groups of equal size.
In our example, after performing the subtractions, the results are multiplied together.
We have:
\((-3) \times 6 = -18\)
  • Notice that a negative number multiplied by a positive number results in a negative number.
Remembering this rule helps in predicting the sign of the product.
This is a critical step and shows how different operations combine in algebra to reach the final solution.

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Most popular questions from this chapter

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