Problem 97 Each calculation below is incorr... [FREE SOLUTION]

Chapter 2: Problem 97

Each calculation below is incorrect. Find the error and correct it. $$ 10-30 = 20 $$

Short Answer

Expert verified

The error was a sign mistake; the correct result is -20.

Step by step solution

Identify the Operation

The given expression is a subtraction: $10 - 30$. Unlike addition or multiplication, subtraction is not commutative, meaning the order of the numbers matters.

Calculate the Correct Result

Subtract 30 from 10, which involves finding the difference. Since 30 is larger than 10, the result will be negative: \[10 - 30 = -20\]

Compare with Given Result

The original given result was $20$. By comparing it to our corrected operation, $-20$, it becomes clear that the error was a sign mistake in the calculation.

Write the Correct Statement

The correct calculation is:\[10 - 30 = -20\]

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Key Concepts

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

Subtraction in Arithmetic

Subtraction is one of the fundamental operations of arithmetic, often signified by the minus sign (-). This operation involves taking away one quantity from another, determining how much more one number is than another. Unlike addition, subtraction is not commutative, meaning swapping the numbers around changes the result. For example, subtracting a larger number from a smaller one leads to a negative result, as seen in this scenario:

For the calculation 10 - 30, you start with 10 and subtract 30.
Since 30 is larger, you end up moving into negative numbers.

This means instead of simply finding the difference, you are calculating how much lesser the initial number is than its subtractor. This operation is essential for finding differences and understanding relationships between numbers.

Negative Numbers

Negative numbers are numbers less than zero, used to represent quantities that go below zeros or indicate opposite directions. On the number line, they appear to the left of zero. They are crucial in representing losses, decreases, or opposites of measured quantities.

When the result of a subtraction operation is less than zero, the outcome is a negative number.
For example, the subtraction 10 - 30 results in -20, which indicates that 10 is 20 units less than 30.

Negative numbers can be tricky initially, but understanding them is vital in many mathematical and real-world contexts, such as calculating debts, temperatures below zero, and altitudes below sea level.

Order of Operations

Order of operations is a fundamental principle that dictates the sequence in which operations should be performed in mathematical expressions, ensuring consistent results. When faced with complex calculations, adhering to this order is crucial:

Always solve expressions inside parentheses first.
Next, exponents are evaluated, followed by multiplication and division from left to right.
Finally, perform addition and subtraction from left to right.

For simple arithmetic involving only subtraction, focus on executing the operation as it appears unless brackets or other signs change the sequence. Failure to follow the appropriate order in mathematical operations can lead to errors, as evidenced in our example of incorrectly identifying the subtraction operation 10 - 30.

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91影视

Each calculation below is incorrect. Find the error and correct it. $$ 10-30 = 20 $$

Short Answer

Step by step solution

Identify the Operation

Calculate the Correct Result

Compare with Given Result

Write the Correct Statement

Key Concepts

Subtraction in Arithmetic

Negative Numbers

Order of Operations

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