Question

Use a number line to find the sum. $$2+(-5)$$

Short answer

-3

Step-by-step solution

Identify the starting point

Begin at the point representing 2 on the number line. This is because the first number in the sum is 2.

Move towards the left of the number line

Since the second number to be added is -5, move 5 steps to the left. Adding a negative number is the same as subtracting a positive number.

Arrive at the resultant number

Upon taking 5 steps to the left from the point representing 2, the point that is reached on the number line represents the sum, 2 + (-5).

Key concepts

Adding Integers

Understanding how to add integers, including negative numbers, is fundamental in math. Integers include all whole numbers and their negative counterparts, such as -3, -2, -1, 0, 1, 2, 3, and so on. When adding two integers, the process depends on the signs of the numbers involved. If both integers have the same sign, add their absolute values and give the sum the shared sign. For example, adding two positive numbers like 3 and 4 is straightforward: 3 + 4 equals 7.

Now, adding a positive integer to a negative integer, like 2 and -5, requires you to consider subtraction. Here's the trick: you subtract the smaller number from the larger one and give the result the sign of the larger number's absolute value. So, for 2 + (-5), you'd subtract 2 from 5 to get 3, and since the larger number is negative, the answer is -3. Remember, the negative sign indicates direction, not just 'less than zero'.

Number Line

A number line is a visual representation of numbers laid out in a straight line, typically with zero at the center, positive numbers extending to the right, and negative numbers extending to the left. It is a powerful tool for understanding integer operations.

To add or subtract integers using a number line:

• Locate your starting point on the line, which is the first number in your equation.
• Move right for adding positive numbers or left for adding negative numbers.
• The number of steps you take corresponds to the absolute value of the second number.

For example, in the exercise 2 + (-5), you start at 2 and move 5 units to the left because you're adding a negative number. The point you land on is -3, which is the sum of 2 and -5.

Subtracting Positive Numbers

Subtracting positive numbers might seem tricky initially, but it follows a logical pattern. When you subtract a positive number, you're moving to the left on the number line. This motion is equivalent to adding a negative number. It's essential to grasp that subtraction of positives is the inverse of adding negatives.

The exercise 2 + (-5) can be thought of as 2 - 5. It's the idea of 'taking away' 5 from 2. By imagining subtraction as backward movement on the number line, it becomes accessible to see why 2 + (-5) lands us at -3. You're taking the 5 steps back from 2, crossing zero, and ending up three spaces into negative territory.