Problem 17 - Algebra 1

Question

Use a number line to find the sum. $$-10+4$$

Step-by-Step Solution

Answer

The sum of -10 and 4 is -6

Step 1: Draw the number line

First, draw a number line. Mark the numbers -10 to 10 on it.

Step 2: Find starting point

Since the first number in the sum is -10, place a point or marker at -10 on the number line. This will be the starting point.

Step 3: Add the second number

The problem asks to add 4 to -10. From the starting point at -10, move 4 units to the right because adding a positive number means moving to the right on the number line.

Step 4: Determine the result

The point will end up on -6, which is the sum of -10 and 4.

Key Concepts

integer addition

Adding integers involves combining positive and negative whole numbers. The number line is a visual tool that helps to better understand this process. When performing integer addition, start at the position of the first number. If the number is negative, you'll start at a point on the left side of zero. If it's positive, you'll start to the right. From there, move right for positive additions and left for negative ones. This exercise uses the example of adding a negative and a positive integer: -10 and 4. By moving four units to the right from -10 on the number line, you find the result, which is -6.

visual learning

A number line is an excellent way for visual learners to grasp math concepts more easily. It provides a clear, straightforward representation of how numbers relate to each other and how calculations are performed.

• Start by drawing a horizontal line.
• Mark evenly spaced numbers, placing zero in the center.
• Use it to visually track the movement during any operation like addition or subtraction.

Visualizing the moves on a number line makes understanding abstract math concepts more intuitive. For instance, the process of adding -10 and 4 becomes a simple matter of moving right from -10.

negative numbers

Negative numbers are found on the left side of zero on a number line. They are the opposite of positive numbers and can initially seem tricky when performing operations like addition. However, using a number line simplifies interactions with negative numbers.
When you add a negative number, essentially, it's like subtracting its absolute value. In contrast, adding a positive number moves the value to the right towards zero if starting from a negative number. In this activity, you started at -10 and added 4. Moving right on the number line ended you up at -6, demonstrating how these movements work with negative numbers.

math problem solving

Effective problem solving in math requires a step-by-step strategy. Start by understanding the problem and identifying the numbers involved. For example, in the problem \(-10+4\) recognize that you're adding a smaller positive number to a larger negative number.

• Visualize the operation using a number line.
• Draw the number line and precisely mark the numbers.
• Place the initial point and move accordingly based on the operation.

After using the number line, double-check to ensure the operations and movements were correctly performed. This approach fosters a deeper understanding of the number system and enhances problem-solving skills.