What is the proper grouping to make the following statement true?
10^2 - 8 + 4 x 3 = 288
To make the statement 10^2 - 8 + 4 x 3 = 288 true, we need to follow the correct grouping or order of operations. The order of operations is as follows: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Let's apply these rules to the given statement:
10^2 - 8 + 4 x 3
First, we evaluate the exponent: 10^2 = 100
Now the statement becomes:
100 - 8 + 4 x 3
Next, we perform multiplication: 4 x 3 = 12
The expression becomes:
100 - 8 + 12
Finally, we perform addition and subtraction from left to right:
100 - 8 + 12 = 92 + 12 = 104
Therefore, the proper grouping to make the statement true is:
(10^2 - 8) + (4 x 3) = 288
To determine the proper grouping to make the statement true, we need to follow the order of operations, also known as PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Let's break down the statement and apply the order of operations:
10^2 - 8 + 4 x 3 = 288
1. Start with the exponent: 10^2 equals 100.
100 - 8 + 4 x 3 = 288
2. Next, perform the multiplication: 4 x 3 equals 12.
100 - 8 + 12 = 288
3. Finally, perform the addition and subtraction from left to right: 100 - 8 equals 92, and 92 + 12 equals 104.
104 = 288
Since 104 does not equal 288, the original statement is false. To make it true, we need to properly group the numbers and operations using parentheses.
One possible way to group the numbers and operations is as follows:
(10^2 - 8 + 4) x 3 = 288
Let's calculate:
(100 - 8 + 4) x 3 = 96 x 3 = 288
Now, the grouping (10^2 - 8 + 4) x 3 makes the statement true.