To understand the given expression [tex]\(10+\frac{1}{4} \times(5+3)-3\)[/tex], let's break it down step by step:
1. Calculate the sum inside the parentheses:
[tex]\[
5 + 3 = 8
\][/tex]
2. Multiply the result by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{1}{4} \times 8 = 2.0
\][/tex]
3. Add 10 to the result:
[tex]\[
10 + 2.0 = 12.0
\][/tex]
4. Subtract 3 from the result:
[tex]\[
12.0 - 3 = 9.0
\][/tex]
So the expression evaluates to 9.0.
Now, let's analyze the statements to determine which one matches our step-by-step solution:
1. "10 more than [tex]\(\frac{1}{4}\)[/tex] of the sum of 5 and 3, then subtract 3":
- This statement correctly describes the steps: First, find the sum of 5 and 3, which is 8. Then take [tex]\(\frac{1}{4}\)[/tex] of that sum, which is 2.0. Add 10 to get 12.0, and finally subtract 3 to get 9.0.
2. "[tex]\(\frac{1}{4}\)[/tex] of 10 times the sum of 5 and 3, minus 3":
- This statement incorrectly suggests multiplying 10 by the sum of 5 and 3, which is not what the expression does.
3. "3 more than 3 plus 5 multiplied by [tex]\(\frac{1}{4}\)[/tex], then add 10":
- This statement incorrectly orders the operations and does not describe the given expression.
4. "10 times [tex]\(\frac{1}{4}\)[/tex] plus 3 and 5, minus 3":
- This statement also incorrectly interprets the expression and order of operations.
Therefore, the correct statement is:
10 more than [tex]\(\frac{1}{4}\)[/tex] of the sum of 5 and 3, then subtract 3.
