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Chapter 1: Problem 64

Select the lesser of the two given numbers. \(|7-2|,|8-1|\)

Short Answer

Expert verified
5

Step by step solution

01

Calculate the first absolute value

First, calculate \(|7-2|\). Subtract 2 from 7 to get 5. The absolute value of 5 is 5.
02

Calculate the second absolute value

Next, calculate \(|8-1|\). Subtract 1 from 8 to get 7. The absolute value of 7 is 7.
03

Compare the results

Compare the two absolute values obtained: 5 and 7. The lesser value between them is 5.

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Key Concepts

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

Absolute Value
Absolute value can be a bit tricky to understand at first, but it boils down to a simple idea: it is the distance a number is from zero on a number line. We write it with two vertical bars, like this: \(|x|\).

The absolute value of a number is always positive or zero because distance cannot be negative.

For instance, both \(|5|\) and \(|-5|\) equal 5. This is because both 5 and -5 are 5 units away from zero. Simple, right?

In our example, we calculated \(|7-2|\) and \(|8-1|\). Both gave us positive values: 5 and 7, respectively. Remember, no matter what鈥檚 inside the absolute value, the result will always be a non-negative number.
Basic Subtraction
Subtraction is one of the first operations in mathematics that we learn. At its core, it's about finding the difference between two numbers.

For subtraction, always take care to subtract the smaller number from the larger one when doing basic problems. This keeps results positive, aligning with our everyday experiences.

In the provided exercise, we performed these subtractions: \(7-2\) and \(8-1\). The steps look like this:
  • 7 minus 2 gives us 5
  • 8 minus 1 gives us 7

These are simple subtracting problems that lead us to our next step involving absolute values.

Note how subtraction set the stage for us to take the absolute values, which we covered earlier!
Comparison of Numbers
Comparison of numbers is essential in determining which number is bigger, smaller, or if they are equal. To compare numbers, we often use symbols like < (less than), > (greater than), and = (equal to).

In the given problem, we are asked to find the lesser absolute value between those obtained from our previous steps. Here it is simple: we know from our steps that 5 and 7 are the absolute values we鈥檝e got.

To compare, you simply ask, which number is smaller?
  • 5 is less than 7

Thus, we concluded that 5 is the lesser of the two numbers.

Understanding comparisons help in many math problems and is useful in real-life situations too, like comparing prices or measurements.

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Most popular questions from this chapter

Solve each problem. Among entertainment expenditures, the average annual spending per U.S. household on fees and admissions was \(\$ 526\) in 2001 . This amount decreased \(\$ 32\) by 2003 and then increased \(\$ 112\) by \(2006 .\) What was the average household expenditure for fees and admissions in \(2006 ?\)

Solve each problem. Linda Des Jardines owes \(\$ 870.00\) on her MasterCard account. She returns two items costing \(\$ 35.90\) and \(\$ 150.00\) and receives credit for these on the account. Next, she makes a purchase of \(\$ 82.50\) and then two more purchases of \(\$ 10.00\) each. She makes a payment of \(\$ 500.00 .\) She then incurs a finance charge of \(\$ 37.23 .\) How much does she still owe?

Solve each problem. In \(1998,\) undergraduate college students had an average (mean) credit card balance of 1879. The average balance increased \(\$ 869\) by 2000 , then dropped \(\$ 579\) by \(2004,\) and then increased \(\$ 1004\) by \(2008 .\) What was the average credit card balance of undergraduate college students in \(2008 ?\)

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 6 if it is divisible by both 2 and \(3,\) and not otherwise. Show that (a) \(1,524,822\) is divisible by 6 and \((b) 2,873,590\) is not divisible by 6

Write a numerical expression for each phrase and simplify. The sum of 12 and \(-7,\) decreased by 14
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