Problem 16 - Prealgebra

Question

Subtract. $$-3-(-10)$$

Step-by-Step Solution

Answer

The result of \(-3 - (-10)\) is \(7\).

Step 1: Understand the Problem

We need to subtract \(-10\) from \(-3\). This is written as \(-3 - (-10)\). When you see a subtraction like this, you need to consider how subtraction and negative signs interact.

Step 2: Apply Rule for Subtracting Negatives

When subtracting a negative number, it is equivalent to adding the positive of that number. So, \(-3 - (-10)\) becomes \(-3 + 10\).

Step 3: Perform the Addition

Now we simply add \(-3\) and \(+10\). Think of this on a number line: starting at \(-3\), if you add \(10\), you move 10 steps to the right, arriving at \(7\).

Step 4: Verify the Calculation

Carefully check the arithmetic again: from \(-3\), adding \(10\) does indeed take you to \(7\). Always verify by reconsidering what adding and steps on a number line would mean.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero, expressed with a minus sign [-]. They are used to represent a deficiency, a decrease, or an opposite direction in various contexts. For example, [-3] is three units less than zero. While positive numbers indicate a certain quantity, moving to negative numbers can be thought of as owing instead of having.

Working with negative numbers is crucial in mathematics and real life. They commonly appear in scenarios such as financial deficits, temperatures below freezing, or measurements below sea level.

Here are a few key points about negative numbers:

• Negative numbers are always less than zero.
• When moving towards zero, negative numbers become less negative (e.g., [-2] is greater than [-3]).
• Adding a negative number is equivalent to subtracting a positive number.
• Subtracting a negative number is the same as adding a positive number.
  
  Mastering negative numbers can help ease the transition into understanding more complex mathematical concepts.

Subtraction Rules

Subtraction can be visualized as uncovering 'how much more' or 'how much less' one number is compared to another. When combined with negative numbers, understanding subtraction rules aids in simplifying expressions.

When faced with subtracting negative numbers, things can seem a bit tricky, but there's a simple rule:

• Subtracting a negative number is the same as adding its opposite positive number.

That means if you see [-3 - (-10)], you can change it to [-3 + 10]. The operation changes from subtraction to addition.

Another useful rule is that subtracting a larger number from a smaller one gives a negative result, reflecting how much the smaller number is lacking when compared to the larger number.

Always double-check your steps when applying these rules, ensuring that mathematical operations are properly followed. This will build accuracy and confidence in solving these types of problems.

Number Line Addition

Number lines are a fundamental visual tool in maths, allowing us to naturally see the interactions between numbers. When dealing with addition and subtraction, the number line helps provide clarity by letting you visualize movements.

In our example problem, [-3 + 10], imagine starting at [-3] on a number line. To solve this operation, follow these steps:

• Identify [-3] on the number line. This is your starting point.
• Now, add [10]: move 10 steps to the right. Every step towards the positive side represents an increase.
• Reaching [7] confirms the result of the operation.

Number line addition effectively demonstrates how subtracting a negative number (convert it to addition) simply moves us to the right. Substantial practice with a number line will develop a strong mental picture, aiding in solving more complex arithmetic operations efficiently.