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Chapter 10: Problem 46

Add. Do not use the number line except as a check. $$ -10.3+(-7.5)+3.1 $$

Short Answer

Expert verified
-14.7.

Step by step solution

01

- Group and Combine Negative Numbers

First, identify and group the negative numbers together. Here, the negative numbers are Step 2 - Combine all numbers -10.3 and -7.5. Combine these numbers by adding them together: Step 3 -10.3 + (-7.5) = -17.8. Add the result from Step 1 to the positive number..
02

- Combine the Results from Step 1 with the Remaining Number

Take the result from Step 1 and add 3.1 to it. (-17.8) + 3.1. Perform the addition:(-17.8) + 3.1 = -14.7.
03

- Verify the Answer using the Number Line (Optional)

To ensure correctness, you can use a number line to check your answer. Start at -10.3, move 7.5 units to the left, and then move 3.1 units to the right. You should end up at -14.7.

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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 a vital concept in mathematics. They represent values less than zero, commonly seen in contexts like temperatures below freezing or financial debts.
Negative numbers are denoted by a minus sign (-) in front of the value. For instance, -7.5 means 7.5 units below zero.
When working with negative numbers, remember:
  • Adding a negative number means moving left on the number line.
  • Subtracting a negative number is like adding a positive number; it moves you to the right on the number line.
Grouping Numbers
Grouping numbers is a helpful strategy in arithmetic, especially when dealing with a mix of positive and negative numbers.
By grouping like terms鈥攑ositive with positive and negative with negative鈥攜ou simplify the computation.
In our example, -10.3 and -7.5 are both negative. By combining these first, you handle similar quantities together, reducing complexity. The initial grouping results in -17.8, which is easier to add to the positive number 3.1.
This approach minimizes errors and streamlines the calculation process. Always look out for opportunities to group numbers effectively.
Number Line
A number line is a visual tool that helps understand the positions and relationships between numbers.
It is a straight line where each point corresponds to a number, with zero in the middle, positive numbers to the right, and negative numbers to the left.
Using a number line:
  • Start at the first number: In our case, -10.3.
  • Move left for negative additions: From -10.3, move 7.5 units left, reaching -17.8.
  • Move right for positive additions: From -17.8, move 3.1 units right, ending at -14.7.
This method visually confirms that the calculation is accurate, reinforcing understanding of how combining different numbers affects the result.

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Most popular questions from this chapter

Simplify. $$ \frac{19-17^{2}}{13^{2}-34} $$

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Find the reciprocal. $$ 13 $$

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Multiply. \(-8 \cdot(-1.3) \cdot(-5)\)
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