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Chapter 2: Problem 27

Find each difference. $$-7-(-10)$$

Short Answer

Expert verified
The difference is 3.

Step by step solution

01

Rewrite the Expression

First, notice that the expression \(-7 - (-10)\) involves subtracting a negative number. Subtracting a negative is the same as adding the positive of that number. Hence, rewrite the expression as \(-7 + 10\).
02

Perform the Addition

Now add the numbers from the rewritten expression. Using the expression from Step 1, perform the addition: \(-7 + 10 = 3\).
03

Verify Your Result

To verify, think about it on the number line. Starting at \(-7\), adding \(10\) moves you 10 units to the right, landing you at \(3\). Therefore, the calculated result is correct.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero. They often represent values like debts, temperatures below freezing, or elevations below sea level. Understanding negative numbers is crucial because they allow us to perform a broader range of calculations.
  • Negative numbers are often denoted with a minus sign (e.g., -5).
  • Surprising to some, negative numbers can be added to and subtracted from other numbers, both positive and negative.
  • Subtracting a negative number is equivalent to adding its positive counterpart.
In the context of the exercise, when you see \(-7 - (-10)\), you're actually working with negative numbers to find their difference. Changing subtraction of a negative to addition of a positive helps simplify calculations.
Number Line
A number line is a simple yet powerful visual tool that helps understand integer operations. It is a horizontal line where numbers are positioned at even intervals.
  • The center of a typical number line is zero, with positive numbers to the right and negative numbers to the left.
  • To exhibit subtraction like in the exercise, start at the number you are subtracting from (move to the left when subtracting a positive number). However, when subtracting a negative number, move to the right.
In the given exercise, visualizing the equation \(-7 - (-10)\) on a number line, you first identify \(-7\) and then add \(+10\), effectively moving to the right by 10 units. This visual tracking confirms the calculation, showing that you end at 3.
Addition of Integers
Addition of integers involves combining values. This can be done using both positive and negative numbers. When adding integers:
  • If you add a positive number to another positive number, the total increases.
  • If you add a negative number, or subtract a positive one, the total decreases.
  • If you subtract a negative number, it's the same as adding a positive, which increases the total.
For the exercise, converting subtraction of a negative to addition makes the operation easier to handle: \(-7 - (-10)\) becomes \(-7 + 10\). Adding 10 to \(-7\) means you鈥檙e moving to the right on a number line, thus getting a positive result of 3.

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Most popular questions from this chapter

At 8: 00 P.M., a temperature of \(78^{\circ} \mathrm{F}\) was recorded. The temperature then changed at an average rate of \(-2^{\circ} \mathrm{F}\) per hour for a 15 -hour period. What was the temperature in degrees Fahrenheit at 7: 00 A.M.?

Evaluate each expression if \(a=0, b=3,\) and \(c=-4\) $$|a b|+b$$

Evaluate each expression. \(a b,\) if \(a=9\) and \(b=8\)

Find the value of each expression. $$2 \times(5+8)-6$$

During a drought, the amount of water in a pond changes by \(-9\) gallons per day due to evaporation. Which of the following tools might you use to find the number of days it takes for the amount of water in a pond to change by \(-108\) gallons of water? Justify your selection(s). Then use the tool(s) to solve the problem.
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