Problem 55
Question
Find the value of each of the following. Use a calculator to check each result. $$ -1(6-1) $$
Step-by-Step Solution
Verified Answer
The value is -5.
1Step 1: Solve inside the parentheses
Start by calculating the expression inside the parentheses. The expression is \(6 - 1\). Perform the subtraction to get \(5\).
2Step 2: Apply the outside factor
Having solved the inner expression, the problem now reads \(-1 \times 5\). Multiply \(-1\) by \(5\) to get \(-5\).
3Step 3: Verify with a calculator
To ensure the solution is correct, enter \(-1 \times (6 - 1)\) into a calculator. The calculator should also display \(-5\).
Key Concepts
Order of OperationsParentheses in MathematicsUsing a Calculator for Verification
Order of Operations
The order of operations is a crucial concept in mathematics that dictates the sequence in which calculations should be carried out. It ensures consistent and accurate results for mathematical expressions. The common mnemonic for remembering this order is PEMDAS, which stands for:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Parentheses in Mathematics
Parentheses are used in mathematics to group numbers and operations. They signify that the operations contained within them should be performed first. This is because operations inside parentheses take precedence due to the order of operations rule.
In the example expression \(-1(6-1)\), the parentheses show that the subtraction must be completed before multiplication. This allows you to first determine the accurate value to substitute back into the rest of the expression. So, \(6 - 1 = 5\), and then the expression becomes \(-1 \times 5\).
This use of parentheses helps to clarify the order in which operations will take place and can often simplify complex expressions by breaking them down into more manageable parts. They guide the reader on which steps are priorities in multi-layered equations.
In the example expression \(-1(6-1)\), the parentheses show that the subtraction must be completed before multiplication. This allows you to first determine the accurate value to substitute back into the rest of the expression. So, \(6 - 1 = 5\), and then the expression becomes \(-1 \times 5\).
This use of parentheses helps to clarify the order in which operations will take place and can often simplify complex expressions by breaking them down into more manageable parts. They guide the reader on which steps are priorities in multi-layered equations.
Using a Calculator for Verification
In mathematics, using a calculator for verification is a helpful step to confirm your manual calculations. After solving an expression by hand, entering the same expression into a calculator can ensure that no errors were made.
With our example, to verify \(-1(6-1)\), input the whole expression exactly as it is into your calculator. This means including parentheses to keep the operations organized according to their priority. The calculator should display \(-5\) as with the manual calculation.
Using a calculator can be particularly beneficial for more complex calculations or when double-checking your results in exams or homework. It gives you peace of mind knowing your work is correct and helps build confidence in your arithmetic skills.
With our example, to verify \(-1(6-1)\), input the whole expression exactly as it is into your calculator. This means including parentheses to keep the operations organized according to their priority. The calculator should display \(-5\) as with the manual calculation.
Using a calculator can be particularly beneficial for more complex calculations or when double-checking your results in exams or homework. It gives you peace of mind knowing your work is correct and helps build confidence in your arithmetic skills.