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Chapter 5: Problem 126

Subtract: \(-4.6-(-10.2)\)

Short Answer

Expert verified
The result is \( 5.6 \)

Step by step solution

01

Rewrite the Problem

The problem can be rewritten as \( -4.6 + 10.2 \) because subtracting a negative number is the same as adding the absolute value of that number.
02

Perform the Addition

With the new expression, calculate the sum: \( -4.6 + 10.2 = 5.6 \)
03

State the Result

The result of \( -4.6 - (-10.2) \) is \( 5.6 \)

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers less than zero, often represented with a minus sign (-) in front of them. This concept is important as it extends the number line to the left of zero. Imagine temperatures dipping below freezing; these are examples of negative numbers in real life.
Handling negative numbers correctly is essential in mathematical operations like subtraction and addition. When you subtract negative numbers, the double negative turns into a plus. For instance,
  • Subtracting -10.2 is equivalent to adding 10.2.
  • This is why the problem in the exercise is rewritten from \(-4.6 - (-10.2)\) into \(-4.6 + 10.2\).
This might seem tricky at first, but once you get used to the concept, these operations become intuitive.
Decoding Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a positive number or zero. Represented by two vertical lines around the number, for example,
  • \(|-4.6| = 4.6\)
  • \(|10.2| = 10.2\)
In subtraction, understanding absolute value helps us correctly switch subtraction of a negative number into an addition operation. In the exercise, when we subtract -10.2, we essentially add its absolute value, 10.2.
Always remember, the absolute value disregards the direction of the number. It provides a simplified way to handle negative numbers in calculations by focusing on the magnitude rather than the direction.
Simplifying Processes with Addition
Addition is the process of combining two or more numbers to get a sum. It is one of the fundamental arithmetic operations and is generally considered straightforward when dealing with positive numbers. But it becomes intriguing when negative numbers are involved.
In the exercise, the subtraction of a negative number \(-4.6 - (-10.2)\) turns into an addition, \(-4.6 + 10.2\), because adding 10.2 is more intuitive. This technique simplifies complex problems by turning them into a familiar addition problem.
  • When dealing with both positive and negative numbers, each numeral's sign (positive or negative) affects the total.
  • If two numbers have the same sign, their absolute values are added, and their common sign is retained.
  • If they have different signs, as in our case, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value.
This understanding transforms potentially confusing operations into manageable steps, making the solutions cleaner and easier to understand.

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Most popular questions from this chapter

When dividing a binomial into a polynomial with missing terms, explain the advantage of writing the missing terms with zero coefficients.

Find the absolute value: \(|-20.3|\)

Subtract \(x^{3}-2 x^{2}+2\) from the sum of \(4 x^{3}+x^{2}\) and \(-x^{3}+7 x-3\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If polynomial division results in a remainder of zero, then the product of the divisor and the quotient is the dividend.

Use a graphing utility to determine whether the divisions have been performed correctly. Graph each side of the given equation in the same viewing rectangle. The graphs should coincide. If they do not, correct the expression on the right side by using polynomial division. Then use your graphing utility to show that the division has been performed correctly. $$\frac{x^{2}-4}{x-2}=x+2$$
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