Problem 41 - Algebra 1

Question

Evaluate the expression. $$ -7+42-63 $$

Step-by-Step Solution

Answer

The evaluation of the arithmetic expression -7 + 42 - 63 is -28.

Step 1: Identify the Operations

The operations given in the exercise are three: two subtractions (-7 and -63) and one addition (+42).

Step 2: Perform the Operations

Firstly, add the negative number -7 to the positive number 42, the result is 35. Secondly, subtract 63 from the previously calculated sum (35).

Step 3: Evaluate

The evaluation of 35 - 63 gives a result of -28.

Key Concepts

Addition

Addition is a fundamental arithmetic operation. It's all about combining numbers to find the total. When you think of adding, you're imagining things coming together to make a bigger number.
Imagine you have 42 apples, and you add 7 more (even if they are a little shrunken!). This action is essentially what addition is. Even though in this case, you're adding 7 negative apples to a positive amount, it still works under the same principle.

Here are some key points to remember:

• The order of addition doesn't matter, so you can add either number first.
• Adding a negative number is like subtracting.
• To add numbers, line them up and bring them together to see the result.

In the context of our exercise, when you added -7 to 42, you were essentially finding how far or close -7 is from 42. The result, 35, is reached by counting down from 42 by 7 units.

Subtraction

Subtraction is the operation used to determine how much is left when some amount is taken away from another. It's the opposite of addition, so when you subtract, you are essentially 'removing' or 'taking away'.
When you subtract a bigger number from a smaller number, like 63 from 35 in the exercise, you dive into negative numbers.

Here are a few things to keep in mind with subtraction:

• It's important to start with the correct number on top.
• The order of numbers in subtraction matters unlike addition.
• If the result of subtraction is less than zero, you've entered the world of negative numbers.

In our example, 35 - 63 leads to -28. This means if you start with 35 and 'take away' 63, you end up 28 below zero on the number line.

Negative Numbers

Negative numbers can sometimes be a tricky concept, but they are just as important as positive numbers. They represent a value less than zero and can be thought of as debts or temperatures below zero.
Negative numbers are usually represented with a minus sign in front. In math, working with negative numbers involves understanding how they interact in operations like addition and subtraction.

Key insights into negative numbers include:

• Negative numbers are always found to the left of zero on a number line.
• When you add a negative number, you move to the left on the number line.
• Negative and positive numbers can cancel each other out when added.

In the final step of our example, having a result of -28 demonstrates that the calculations led to a position 28 steps to the left of zero on the number line. It shows that after all additions and subtractions, the balance tips into a negative.