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Chapter 1: Problem 23

Evaluate each of the following expressions, if possible. $$5-3-7$$

Short Answer

Expert verified
-5

Step by step solution

01

Simplify the First Subtraction

Evaluate the first subtraction operation. Calculate the result of \(5-3\).$$5-3 = 2$$
02

Perform the Remaining Subtraction

Now subtract the result from step 1 by 7. Calculate \(2-7\).$$2-7 = -5$$
03

Confirm the Result

Check the calculations to ensure they were performed correctly and verify that the final result is indeed $$-5$$.

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Key Concepts

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

Integer Subtraction
Integer subtraction is the operation of taking one integer away from another. This is a fundamental skill in elementary algebra. When you're subtracting, it's helpful to think of the number line.
With integer subtraction, the direction matters:
  • Subtracting a smaller number from a larger one moves you to the left on the number line, resulting in a positive integer.
  • Subtracting a larger number from a smaller one moves you further left, past zero, into the negative integers.
For example, in the expression \(5-3-7\), we first compute \(5-3=2\). Then we subtract 7 from 2, resulting in \(2-7=-5\). Remember, moving left from 2 by 7 steps takes us into negative territory, so we get \(-5\). Using a number line visualization can help solidify this concept.
Order of Operations
The order of operations dictates the sequence in which operations should be performed to ensure accurate results. This is especially important in expressions with multiple operations.
In mathematics, we use the acronym PEMDAS to remember the order:
  • \textbf{P}: Parentheses first
  • \textbf{E}: Exponents (i.e., powers and roots)
  • \textbf{MD}: Multiplication and Division (from left to right)
  • \textbf{AS}: Addition and Subtraction (from left to right)
For subtraction only, like in our example \(5-3-7\), follow the operations from left to right.
Calculate \(5-3\) first to get \(2\).
Then, subtract 7 from 2, resulting in \(-5\). Ensuring you follow these steps in order helps prevent mistakes.
Negative Numbers
Negative numbers are numbers less than zero, used to represent a deficiency or loss. They are essential for solving many mathematical problems.
Negative numbers lie to the left of zero on the number line. When subtracting a larger number from a smaller one, the result is a negative number.
In the example \(5-3-7\), after simplifying to \(2-7\), we enter the realm of negative numbers.
  • Subtract 2 minus 7, starting from 2 and moving left 7 steps on the number line.
  • You go past zero and land at \(-5\).
Understanding how negative numbers operate is key in algebra. It ensures accuracy when handling more complex equations later on.

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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. $$2 \frac{1}{3}$$

Graph the given set on a number line. \(\\{x | x \text { is an even natural number less than } 10\\}\)

In Exercises \(73-84\), evaluate the given expression. $$|-4-3+2|-4-3+2$$

Sketch the given set on a number line. $$\\{x | x<-2\\}$$

Let set \(A\) be the first ten multiples of 2 and let set \(B\) be the first ten multiples of 3\. Let \(C\) be the set of numbers both sets have in common. How would you describe set \(C\) ?
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