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Chapter 3: Problem 493

In the following exercises, simplify. $$ 10-(5-6) $$

Short Answer

Expert verified
The simplified expression is 11.

Step by step solution

01

Understand the expression

The expression to simplify is: \(10 - (5 - 6)\). Notice there is a parentheses which is embedded inside the expression.
02

Simplify the inner parentheses

First solve inside the parentheses: \(5 - 6\). \(5 - 6 = -1\). Replace \(5 - 6\) with \(-1\) in the expression, resulting in: \(10 - (-1)\).
03

Simplify the expression

Now, simplify the expression \(10 - (-1)\). Subtracting a negative number is equivalent to adding that number: \(10 - (-1) = 10 + 1\). Then, \(10 + 1 = 11\).

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Key Concepts

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

mathematical expressions
Mathematical expressions are combinations of numbers, variables, and operators that represent a specific value. Expressions can be simple or complex and are often used to convey mathematical relationships and operations. In prealgebra, learning how to interpret and manipulate these expressions is crucial. For example, the expression in our problem is: \(10 - (5 - 6)\). This expression uses numbers and the subtraction operator. Understanding how to break down and simplify such expressions step-by-step is essential to becoming proficient in math.
simplifying expressions
Simplifying expressions involves reducing them to their simplest form. This process often includes combining like terms and performing operations within parentheses. In our exercise, the expression is \(10 - (5 - 6)\). Here鈥檚 how to simplify it:
  • First, identify and simplify the inner parentheses: \(5 - 6\). This equals \(-1\). Replace \(5 - 6\) with \(-1\), resulting in \(10 - (-1)\).
  • Next, simplify the expression without the parentheses: \(10 - (-1)\). Remember that subtracting a negative number is the same as adding the positive equivalent. So, \(10 - (-1)\) turns into \(10 + 1\).
  • Finally, perform the addition: \(10 + 1 = 11\).
These steps break down the simplification process, giving you a clear path from the original expression to the simplified result.
negative numbers
Negative numbers represent values less than zero and are denoted with a minus sign (-). They can initially be confusing, especially when involved in operations like subtraction. In our exercise, you encounter \(10 - (-1)\). Here鈥檚 how to handle negative numbers:
  • When subtracting a negative number, it turns into the addition of its positive counterpart. For instance, subtracting \(-1\) is the same as adding \(+1\).
  • So, \(10 - (-1)\) simplifies to \(10 + 1\). This transformation helps prevent errors when dealing with negative signs.
  • Knowing these basics about negative numbers will strengthen your algebra skills and make solving expressions more intuitive.
Always be mindful of the negative signs and apply these rules to simplify mathematical expressions accurately.

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