Chapter 15: Problem 30
Simplify. $$ -10-2.68 $$
Short Answer
Expert verified
-12.68
Step by step solution
01
Understand the problem
The problem requires simplifying the expression -10-2.68 . This is a basic operation involving subtraction of a decimal number from a negative integer.
02
Rewrite the expression
Rewrite the expression to make it easier to understand: -10 - 2.68 . This shows clearly that you are subtracting 2.68 from -10.
03
Combine the numbers
Combine the numbers by thinking of moving further left on the number line: -10 - 2.68 = -10.00 - 2.68 = -12.68 .
04
Simplified result
The simplified result of the expression -10 - 2.68 is -12.68 .
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
decimal subtraction
Decimal subtraction involves subtracting numbers that include decimals, which can be a bit tricky when you're dealing with different digit lengths. To perform decimal subtraction correctly, follow these steps:
1. **Align the Decimal Points**: Always line up the numbers so that the decimal points are vertically aligned. This helps in accurately subtracting each column of digits.
2. **Subtract from Right to Left**: Start from the rightmost digit and move left, borrowing as necessary. If a column in the minuend (the top number) is smaller than the subtrahend (the bottom number), you'll need to borrow from the next column to the left.
3. **Place the Decimal Point in the Answer**: The result should also have a decimal point directly beneath the other decimal points in the original numbers.
Let's look at our example: \-10 - 2.68. First, write -10 as -10.00 to align the decimal points:
\[ -10.00 - 2.68 \]
Subtract as you would with regular numbers, but remember to bring the decimal point straight down into your answer:
\[ -12.68 \]
This is how you correctly perform decimal subtraction.
1. **Align the Decimal Points**: Always line up the numbers so that the decimal points are vertically aligned. This helps in accurately subtracting each column of digits.
2. **Subtract from Right to Left**: Start from the rightmost digit and move left, borrowing as necessary. If a column in the minuend (the top number) is smaller than the subtrahend (the bottom number), you'll need to borrow from the next column to the left.
3. **Place the Decimal Point in the Answer**: The result should also have a decimal point directly beneath the other decimal points in the original numbers.
Let's look at our example: \-10 - 2.68. First, write -10 as -10.00 to align the decimal points:
\[ -10.00 - 2.68 \]
Subtract as you would with regular numbers, but remember to bring the decimal point straight down into your answer:
\[ -12.68 \]
This is how you correctly perform decimal subtraction.
negative numbers
Negative numbers are numbers less than zero, often representing a loss or a position below a reference point. When dealing with negative numbers in subtraction, there are a few key points to understand:
1. **Subtracting a Positive from a Negative**: When you subtract a positive number from a negative one, you're moving further left on the number line. This means the result will be a more negative number.
2. **Example**: In our exercise, \-10 - 2.68, you're taking an already negative number (-10) and subtracting a positive decimal (2.68). This pushes the result further into the negative:
\[ -10 - 2.68 = -12.68 \]
This concept is crucial in simplifying expressions involving negative and decimal numbers.
Understanding how negative numbers interact makes solving more complex problems easier.
1. **Subtracting a Positive from a Negative**: When you subtract a positive number from a negative one, you're moving further left on the number line. This means the result will be a more negative number.
2. **Example**: In our exercise, \-10 - 2.68, you're taking an already negative number (-10) and subtracting a positive decimal (2.68). This pushes the result further into the negative:
\[ -10 - 2.68 = -12.68 \]
This concept is crucial in simplifying expressions involving negative and decimal numbers.
Understanding how negative numbers interact makes solving more complex problems easier.
number line
A number line is a visual representation of numbers placed in order on a straight line. It’s very helpful for visualizing arithmetic operations involving positive and negative numbers.
1. **Positive and Negative Moves**: On a number line, moving to the right indicates addition, while moving to the left indicates subtraction.
2. **Using Number Line for Our Problem**: Consider -10 on the number line. When you subtract 2.68 from -10, you're moving 2.68 units to the left. This process helps us see that we end up further in the negative zone:
\[ -12.68 \]
3. **Visual Aid**: Visualizing the problem on a number line clarifies why subtracting a positive number from a negative one results in a more negative number.
Using a number line is a valuable technique to understand and solve problems involving decimal subtraction and negative numbers.
1. **Positive and Negative Moves**: On a number line, moving to the right indicates addition, while moving to the left indicates subtraction.
2. **Using Number Line for Our Problem**: Consider -10 on the number line. When you subtract 2.68 from -10, you're moving 2.68 units to the left. This process helps us see that we end up further in the negative zone:
\[ -12.68 \]
3. **Visual Aid**: Visualizing the problem on a number line clarifies why subtracting a positive number from a negative one results in a more negative number.
Using a number line is a valuable technique to understand and solve problems involving decimal subtraction and negative numbers.