Problem 40 - Prealgebra

Question

Add the following numbers left to right. $$35+(-5)+(-30)$$

Step-by-Step Solution

Answer

The sum is 0.

Step 1: Address the First Two Numbers

Begin by adding the first two numbers: 35 and -5. We start with 35 and subtract 5, because adding a negative number is the same as subtraction. \[ 35 + (-5) = 35 - 5 = 30 \]

Step 2: Add the Result to the Last Number

Next, take the result from Step 1, which is 30, and add it to -30. This is another subtraction, where 30 minus 30 gives:\[ 30 + (-30) = 30 - 30 = 0 \]

Step 3: Conclusion

The final result after performing these operations sequentially from left to right is 0.

Key Concepts

Understanding Negative Numbers

Negative numbers often represent values less than zero, such as a financial debt or loss of temperature below freezing. These numbers are denoted with a minus sign (-) in front of them.
When working with negative numbers:

• Adding a negative number is like subtracting the positive value of that number. For example, when you see \( -5 \), you can think of it as subtracting \( 5 \).
• Subtracting a negative number is equivalent to adding its positive counterpart. For example, \( 10 - (-2) \) becomes \( 10 + 2 \).

Understanding how negative numbers impact addition and subtraction can significantly simplify solving equations.

Adding Integers

Adding integers, including both positive and negative numbers, might seem tricky at first, but it follows simple rules. When dealing with integers:

• If you add two positive numbers, the result is positive.
• Adding two negative numbers yields a negative result. Imagine adding debts, \(-3 + (-5) = -8 \).
• Combining a positive and a negative integer involves subtracting the smaller absolute value from the larger one and taking the sign of the number with the larger absolute value.

For example, in the equation \( 35 + (-5) \), start with \( 35 \) and subtract \( 5 \), resulting in \( 30 \). Practice these principles to handle any mix of integers.

Grasping the Order of Operations

When faced with an expression involving multiple operations, it's essential to perform them in a specific order, famously remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

• Always handle calculations inside parentheses first.
• Next, deal with exponents.
• Then, move from left to right performing any multiplications or divisions as they appear.
• The final step is to perform any additions or subtractions, moving again from left to right.

In the task of adding \( 35 + (-5) + (-30) \), you only have additions and no parentheses or exponents. Simply work from left to right, adding the numbers step by step, first tackling \( 35 + (-5) \) and then adding \(-30\) to the result. This proper handling ensures accuracy at every stage.