Question

Use a number line to find the sum. $$2+(-9)+3$$

Short answer

The sum of 2, -9, and 3 is -4.

Step-by-step solution

Represent First Number on Number Line

Start by representing the first number, which is 2, on the number line. Put a dot on the number line at the point 2.

Add the Negative Integer

To add the negative integer -9, move 9 steps to the left from the point 2 on the number line. This is because adding a negative number is equivalent to subtracting the absolute value of that number. This step takes you to the point -7.

Add the Final Number

Next, add the final number, which is 3. This involves moving 3 steps to the right from the point -7 on the number line. This takes you to the point -4.

Key concepts

Adding Integers

Understanding addition on the number line is crucial for mastering arithmetic operations. When adding integers, whether positive or negative, we can visualize this process on a number line to clarify the concept.

Addition of positive integers means moving to the right on the number line. For example, starting from zero and adding 5 would bring us to the point marked as 5. However, when we add a negative integer, such as -3, it's like adding a 'debt' to our current position, moving us 3 steps to the left instead. This is why adding -3 to 5 would bring us back to the point marked as 2. The key is remembering that 'left means minus', and 'right means plus' on the number line.

Utilizing this visualization aids students in grasping the abstract concept of adding integers, turning it into a manageable, almost physical, action of moving along a line.

Negative Integers

Negative integers can often be a source of confusion, but they don't have to be. Think of negative numbers as the opposite of positive numbers, existing on the left side of zero on the number line. They represent values less than zero, such as debts or temperatures below freezing.

When dealing with negative integers in addition, like -9 in our textbook exercise, it's important to understand that they signify a movement to the left when placed on the number line. For students, knowing that negative integers denote a subtraction can simplify complex arithmetic operations and empower them to solve more advanced problems with confidence.

Arithmetic Operations

Arithmetic operations form the foundation of mathematics, with addition being one of the most fundamental. In our exercise, we added different integers together, which showcases the process of combining quantities.

Understanding arithmetic operations includes recognizing patterns and rules, such as 'a negative and a positive make a negative,' or 'two negatives make a positive.' These rules help us navigate through more complicated math problems. An essential aspect of arithmetic is the order of operations, ensuring that we carry out mathematical tasks in the correct sequence to arrive at the right answer.

In summary, a solid grasp of arithmetic operations and the way they interplay with positive and negative integers is vital for students to solve math problems accurately and efficiently.