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Chapter 5: Problem 30

Add or subtract the decimals, as indicated. \(-7.5+(-7.11)\)

Short Answer

Expert verified
The result of adding \(-7.5 + (-7.11)\) is \(-14.61\).

Step by step solution

01

Identify the operation

The exercise asks us to add two negative decimals: \(-7.5\) and \(-7.11\). Since both are negative, we will add their absolute values.
02

Add the absolute values

To add the absolute values of the decimals, we will align the decimal points and add:\[7.50 + 7.11 \]Aligning them, we add digit by digit:- Hundredths: \(0 + 1 = 1\)- Tenths: \(5 + 1 = 6\)- Units: \(7 + 7 = 14\), resulting in 14.61 when combined.
03

Apply the negative sign

Since both original numbers were negative, the result of the addition will also be negative. Thus, the final result is \(-14.61\).

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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. They are often used to represent a loss, decrease, or temperatures below freezing point. In mathematics, they are denoted with a minus sign in front, such as - Examples of negative numbers include - Temperature: - Debt: - Elevations below sea level: Understanding negative numbers is crucial for solving mathematical problems involving temperature changes or financial transactions.
Exploring Addition with Negative Numbers
Addition is a fundamental arithmetic operation. When involving negative numbers, it can seem tricky at first. The key is to understand that adding a negative number is akin to subtracting its absolute value from a positive number. Here鈥檚 a step by step approach: - If you add two negative numbers, you actually add their absolute values and assign the negative sign to the result. For instance, in the expression - If you add a positive and a negative number, you determine which absolute value is larger and subtract the smaller one from the larger. The result takes the sign of the larger absolute value.
Demystifying Absolute Value
Absolute value refers to the non-negative value of a number, regardless of its sign. It measures the distance of a number from zero on the number line. - The absolute value of any number is always positive because distance cannot be negative. - For a negative number, simply remove the minus sign to find its absolute value. Understanding absolute value allows us to simplify calculations when dealing with negative numbers, especially in addition and subtraction tasks.
Mastering Arithmetic Operations Involving Decimals
Arithmetic operations with decimals can initially appear daunting due to the decimal points. However, breaking down the process into simpler steps makes it manageable. Key tips include: - Aligning decimal points ensures accuracy in addition and subtraction. - Remember to carry over in addition or borrow in subtraction as needed, similar to whole number operations. - Always apply the necessary negative or positive sign to the result after completing the operation. By breaking down each operation into steps, decimals become less mystifying and can be handled with ease.

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Most popular questions from this chapter

Your solutions should include a well-labeled sketch. The lengths of two legs of a right triangle are 12 meters and 16 meters. Find the exact length of the hypotenuse.

Compute the exact square root. If the square root is undefined, write "undefined". \(\sqrt{225}\)

Compute the exact square root. \(\sqrt{3.61}\)

A 10-foot ladder leans against the wall of a house. How high will the ladder be if the bottom of the ladder is 4 feet from the wall? Round your answer to the nearest tenth.

Compute the exact square root. If the square root is undefined, write "undefined". \(-\sqrt{25}\)
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