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Chapter 2: Problem 43

Evaluate the expression. $$ 6-1+10-(-8) $$

Short Answer

Expert verified
The final result of the expression is \(23\)

Step by step solution

01

Identifying the expression

The expression to be evaluated is: \(6 - 1 + 10 -(-8)\)
02

Applying addition and subtraction from left to right

Perform the operations of addition and subtraction from left to right: \1. Start with the first operation \(6 - 1\), the result is \(5\). \2. Then, add the 10 to \(5\), the result is \(15\). \3. Lastly, subtracting a negative is equivalent to addition, so you add \(8\) to the total, making the result \(23\).
03

Final answer

After performing all the addition and subtraction expressions, the result is \(23\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Addition
Addition is a fundamental math operation where we find the total sum by combining numbers. It's often represented by the plus sign "+". When we add numbers, we move forward on the number line.
For example, when we add 10 to 5 in the expression, we start from 5 and move 10 steps forward, landing on 15.
  • Simplifying Expressions: In our problem, after simplifying the subtraction, the expression became 5, and adding 10 brought us to 15.
  • Order of Operations: It's important to perform addition step-by-step as the order matters, especially in complex expressions.
Remember, combining terms through addition can change depending on how they are grouped, especially with multiple numbers.
Subtraction
Subtraction, represented by the minus sign "-", means taking away from a number. In subtraction, we move backward on the number line. This operation is crucial to simplifying expressions.
In the expression, we first performed the subtraction operation of 6 - 1. Here, you begin at 6 and move one step back, reaching 5.
  • Left to Right Rule: The expression must be evaluated from left to right. So, take care to follow this order, ensuring correct calculations.
  • Reversing Addition: Always think of subtraction as the opposite of addition. It's about reducing the total amount.
By keenly applying subtraction in the right order, you ensure accurate results and set the stage for the next operations.
Negative Numbers
Negative numbers are positioned to the left of zero on the number line and are represented with a minus "-" sign before them. They play a vital role in various calculations.
In the expression, you encounter -(-8). Here, subtracting a negative number is like adding its positive counterpart.
  • Subtracting Negatives: When confronted with --8, it transforms into +8. This is because double negatives cancel each other, switching the direction to addition.
  • Understanding Symbols: It's essential to recognize these signs and their implications to prevent errors.
By mastering negative numbers, you can handle various expressions confidently and simplify even the most complex problems.

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Most popular questions from this chapter

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ 3(x+4) $$

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ -9(a+6) $$

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ -3(r+8) $$

EXPRESSIONS WITH FRACTION BARS Evaluate the expression. $$ \frac{(2+5)^{2}}{3^{2}-2} $$

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ -3+y+7 $$
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