Final answer:
Using a number line for addition and subtraction allows visualizing movements: right for addition and left for subtraction. The expressions 2 + 3 = 5 for addition and 5 - 3 = 2 for subtraction demonstrate how to use a number line to solve these problems.
Step-by-step explanation:
Using a number line to write and evaluate an addition expression, imagine you're at point 2 and you want to add 3. Start from 2 on the number line, move 3 units to the right, and you'll end at 5. So the addition expression is 2 + 3 = 5.
Now, to write and evaluate a subtraction expression using a number line, suppose you need to subtract 3 from 5. Begin at 5 on the number line, and move 3 units to the left, arriving at 2. This can be represented as the subtraction expression 5 - 3 = 2. Additionally, if you were to subtract a negative number, such as subtracting -3 from 2, the expression becomes 2 - (-3) = 2 + 3 = 5, as subtracting a negative is the same as adding its positive counterpart.
To summarize the basic principles:
- When adding or subtracting whole numbers, pay attention to the direction you move on the number line: right for addition, left for subtraction.
- For addition, like signs result in a sum with that sign, while for unlike signs, subtract the smaller number from the larger and take the sign of the larger number.
- In subtraction, change the sign of the subtracted number and follow the rules for addition.
Applying these principles to vectors, you can use similar methods where vectors in a straight line can be added or subtracted algebraically. When using graphical methods for vector addition and subtraction, it's key to lay out each vector tip-to-tail and determine the resultant vector.