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Chapter 1: Problem 90

What should the answer to \(4-(-7)\) be and why?

Short Answer

Expert verified
The answer to 4 - (-7) is 11 because subtracting a negative number is the same as adding its positive counterpart.

Step by step solution

01

Understand the Problem

The problem involves a subtraction operation where the minuend is 4 and the subtrahend is -7. The task is to find the result of subtracting negative seven from four.
02

Apply the Rule of Subtraction

Subtracting a negative number is equivalent to adding its positive counterpart. Therefore, we convert the expression 4 - (-7) into 4 + 7.
03

Perform the Addition

Add the two numbers: 4 + 7 = 11.
04

State the Final Answer

The result of the operation is 11.

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Key Concepts

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

subtraction rule
When dealing with subtraction in mathematics, especially with integers, it's important to understand the subtraction rule. The rule of subtraction states that subtracting a negative number is the same as adding the absolute value of that number.

To put it simply, if you see an expression like 4 - (-7), you can change it to 4 + 7.

This happens because subtracting a negative is essentially removing a debt, which increases the quantity you have. Remember:
  • 4 - (-7) becomes 4 + 7.
  • -3 - (-5) becomes -3 + 5.
Practicing this rule makes integer operations easier.
negative numbers
Negative numbers can seem tricky at first, but they follow specific rules that make them easy to work with. A negative number is a number that is less than zero, such as -1, -2, and -7.

When plotted on the number line, negatives are to the left of zero.

Here are some key points to keep in mind:
  • Adding a negative number means moving left on the number line.
  • Subtracting a negative number means moving right on the number line.
For example, in the problem 4 - (-7), subtracting -7 moves you right by 7 units on the number line, effectively adding 7 to 4.

Understanding how these numbers interact helps in correctly applying operations.
addition
Addition is one of the fundamental mathematical operations, and it becomes particularly interesting when combined with the rules of negative numbers and subtraction.

In basic terms, addition involves combining two or more numbers to get a total sum: for instance, 3 + 2 equals 5.

When dealing with integer addition:
  • Positive + Positive yields a larger positive number.
  • Negative + Negative yields a larger negative number.
  • Positive + Negative or vice versa involves finding the difference between their absolute values and determining the sign based on the larger absolute value.
In our subtraction problem turned addition problem: 4 + 7, we simply add the two positives to get 11.

Grasping these addition principles makes solving such problems straightforward.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$30-(5 \cdot 4-2)$$

In Exercises \(1-72\), compute the value of each expression. $$52-(-38)-67$$

Evaluate the given expression. Remember to follow the order of operations. $$5+\\{2+4[3+3(4+2)]\\}$$

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

If we denote a debt of \(\$ 15,000\) as \(-\$ 15,000,\) explain how you could use subtraction of negative numbers to represent and calculate the following: Reduce a debt of \(\$ 15,000\) by \(\$ 6,000\)
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