Chapter 0: Problem 61
Evaluate each expression. $$ 4 \cdot(9+5)-6 \cdot 7+3 $$
Short Answer
Expert verified
17
Step by step solution
01
Evaluate Inside the Parentheses
First, evaluate the expression inside the parentheses. Here we have \( 9 + 5 \) which simplifies to \( 14 \).
02
Multiply
Next, multiply the result from Step 1 by 4: \( 4 \cdot 14 \) which equals \( 56 \).
03
Multiply
Following, multiply 6 by 7: \( 6 \cdot 7 \) which equals \( 42 \).
04
Subtract
Now, subtract the result from Step 3 from the result from Step 2: \( 56 - 42 \) which equals \( 14 \).
05
Add
Finally, add 3 to the result from Step 4: \( 14 + 3 \) which equals \( 17 \).
Unlock Step-by-Step Solutions & Ace Your Exams!
-
Full Textbook Solutions
Get detailed explanations and key concepts
-
Unlimited Al creation
Al flashcards, explanations, exams and more...
-
Ads-free access
To over 500 millions flashcards
-
Money-back guarantee
We refund you if you fail your exam.
Over 30 million students worldwide already upgrade their learning with Vaia!
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Order of Operations
When evaluating mathematical expressions, it's crucial to follow the order of operations, sometimes remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This ensures that everyone evaluates the expression in the same way and achieves the same result.
In our example, the process involves:
By following the order of operations, we evaluate complex expressions systematically and accurately.
In our example, the process involves:
- Handling parentheses first
- Performing multiplication next
- Finally, moving on to subtraction and addition
By following the order of operations, we evaluate complex expressions systematically and accurately.
Parentheses
Parentheses are used to indicate which operations should be performed first in an expression. They help in grouping terms and operations that need to be prioritized.
In the given expression, we first encounter the parentheses around \(9 + 5\). According to PEMDAS, we need to solve inside the parentheses first.
So, \(9 + 5 = 14\). This simplifies part of our expression to \(4 \cdot 14 - 6 \cdot 7 + 3\). Dealing with parentheses early helps clear up and organize the remaining steps.
In the given expression, we first encounter the parentheses around \(9 + 5\). According to PEMDAS, we need to solve inside the parentheses first.
So, \(9 + 5 = 14\). This simplifies part of our expression to \(4 \cdot 14 - 6 \cdot 7 + 3\). Dealing with parentheses early helps clear up and organize the remaining steps.
Arithmetic Operations
Arithmetic operations include addition, subtraction, multiplication, and division. These are the basic building blocks of math that help us perform calculations.
The given problem requires us to handle multiplication, subtraction, and addition in the right order. Each type of operation has designated steps, and following each step properly leads to the correct result.
Remember to handle each operation separately and in the correct sequence as outlined by the order of operations. This approach minimizes any possible mistakes.
The given problem requires us to handle multiplication, subtraction, and addition in the right order. Each type of operation has designated steps, and following each step properly leads to the correct result.
Remember to handle each operation separately and in the correct sequence as outlined by the order of operations. This approach minimizes any possible mistakes.
Multiplication
Multiplication is one of the primary arithmetic operations and is handled after parentheses but before addition and subtraction.
In our expression, we first found that \(9 + 5 = 14\). Next, we need to multiply this result by 4: \(4 \cdot 14 = 56\). Then, we have another multiplication step, which is \(6 \cdot 7 = 42\).
By completing these multiplication steps accurately and in the correct sequence, we simplify the expression to \(56 - 42 + 3\).
In our expression, we first found that \(9 + 5 = 14\). Next, we need to multiply this result by 4: \(4 \cdot 14 = 56\). Then, we have another multiplication step, which is \(6 \cdot 7 = 42\).
By completing these multiplication steps accurately and in the correct sequence, we simplify the expression to \(56 - 42 + 3\).
Addition
Addition is among the last steps in our order of operations for this particular expression.
First, we handled parentheses and multiplication. After simplifying, we arrived at an expression where subtraction comes next. We subtracted \(42\) from \(56\), giving us \(14\).
Finally, we add \(3\) to \(14\), which wraps up the problem and gives us a final result of \(17\). Addition consolidates our previous steps and concludes the evaluation of the expression.
First, we handled parentheses and multiplication. After simplifying, we arrived at an expression where subtraction comes next. We subtracted \(42\) from \(56\), giving us \(14\).
Finally, we add \(3\) to \(14\), which wraps up the problem and gives us a final result of \(17\). Addition consolidates our previous steps and concludes the evaluation of the expression.
Subtraction
Subtraction is another key arithmetic operation that typically follows multiplication and handles alongside addition.
In the given expression, after completing all parentheses and multiplication steps, we reach \(56 - 42\). Performing this subtraction gives us \(14\).
Subtraction helps us to finalize the value we worked on through the previous steps, and it's crucial to perform it accurately before moving on to any addition. This ensures the final solution is correct.
In the given expression, after completing all parentheses and multiplication steps, we reach \(56 - 42\). Performing this subtraction gives us \(14\).
Subtraction helps us to finalize the value we worked on through the previous steps, and it's crucial to perform it accurately before moving on to any addition. This ensures the final solution is correct.
