Problem 1
Question
For the following problems, simplify the expressions. $$ 12+7(4+3) $$
Step-by-Step Solution
Verified Answer
Answer: 61
1Step 1: Order of operations - Parentheses
According to the order of operations (PEMDAS/BODMAS), we first need to deal with the operation inside the parentheses. In this case, we have (4+3):
$$
12 + 7(4 + 3)
$$
Inside the parentheses:
$$
4 + 3 = 7
$$
So, we can rewrite the expression as:
$$
12 + 7(7)
$$
2Step 2: Order of operations - Multiplication
Now we need to do the multiplication operation:
$$
12 + 7(7)
$$
Multiplication:
$$
7 \times 7 = 49
$$
So, we can rewrite the expression as:
$$
12 + 49
$$
3Step 3: Order of operations - Addition
Finally, we are left with the addition:
$$
12 + 49
$$
Addition:
$$
12 + 49 = 61
$$
The simplified expression is 61.
Key Concepts
Understanding ParenthesesExecuting Multiplication FirstPerforming Addition Last
Understanding Parentheses
In mathematics, parentheses are used to group parts of an expression that should be calculated first. When you see an expression like \(12 + 7(4 + 3)\), the order of operations tells us to start with the parentheses. This is part of the PEMDAS/BODMAS rule, which stands for Parentheses (or Brackets), Exponents (or Orders), Multiplication and Division (left to right), Addition and Subtraction (left to right).
By performing the calculation inside the parentheses first, we simplify the math. In our example, within the parentheses \((4+3)\), we add 4 and 3 together to get 7. This makes the expression easier to handle: \(12 + 7(7)\). Parentheses help clarify which operations need priority, guiding us to the correct solution.
By performing the calculation inside the parentheses first, we simplify the math. In our example, within the parentheses \((4+3)\), we add 4 and 3 together to get 7. This makes the expression easier to handle: \(12 + 7(7)\). Parentheses help clarify which operations need priority, guiding us to the correct solution.
Executing Multiplication First
Once we have dealt with parentheses, the next operation in PEMDAS/BODMAS is multiplication. Consider the expression now at \(12 + 7(7)\). Here, \(7(7)\) signifies that we need to multiply 7 by 7.
Multiplication is a quick way to add a number repeatedly. Essentially, multiplying 7 by 7 is like adding 7, seven times. This gives us 49: \(7 \times 7 = 49\). It's important to complete any multiplication before moving on to other operations, ensuring the proper mathematical order is respected. This changes our expression to \(12 + 49\).
Multiplication is a quick way to add a number repeatedly. Essentially, multiplying 7 by 7 is like adding 7, seven times. This gives us 49: \(7 \times 7 = 49\). It's important to complete any multiplication before moving on to other operations, ensuring the proper mathematical order is respected. This changes our expression to \(12 + 49\).
Performing Addition Last
The last step in our order of operations is addition. With multiplication complete, the expression \(12 + 49\) leaves us only with simple addition.
Addition means calculating the total when two or more numbers are combined. Here, when you add 12 to 49, you get 61. So, \(12 + 49 = 61\).
Addition means calculating the total when two or more numbers are combined. Here, when you add 12 to 49, you get 61. So, \(12 + 49 = 61\).
- This step might seem straightforward, but it’s crucial to do it last to avoid errors.
- Remember, in PEMDAS/BODMAS, addition is among the final operations unless specified otherwise.
Other exercises in this chapter
Problem 1
Find each product. $$ x^{2} \cdot x^{5} $$
View solution Problem 1
Simplify each expression using the power rule for powers. $$ \left(x^{5}\right)^{4} $$
View solution Problem 1
Write each of the following using exponents. \(a \cdot a \cdot a \cdot a\)
View solution