Let's carefully analyze the expression [tex]\(\left(\frac{1}{4} \times 8 + 3\right) \div 5\)[/tex] step by step to determine the correct description of the expression.
1. Inner Multiplication:
- We start with the fraction [tex]\(\frac{1}{4}\)[/tex] and multiply it by 8:
[tex]\[
\frac{1}{4} \times 8 = 2.0
\][/tex]
2. Addition:
- Then, we add 3 to the result of the multiplication:
[tex]\[
2.0 + 3 = 5.0
\][/tex]
3. Division:
- Finally, we divide the result of the addition by 5:
[tex]\[
\frac{5.0}{5} = 1.0
\][/tex]
So, the expression [tex]\(\left(\frac{1}{4} \times 8 + 3\right) \div 5\)[/tex] evaluates to 1.0.
Now, let's match this detailed step-by-step calculation to the given statements:
- Statement 1: "Add three to the quotient of [tex]\(\frac{1}{4}\)[/tex] and 8 , then divide by 5"
- This is incorrect. The expression does not involve finding the quotient of [tex]\(\frac{1}{4}\)[/tex] and 8.
- Statement 2: "Add 3 to the sum of [tex]\(\frac{1}{4}\)[/tex] and 8 , then divide by 5"
- This is incorrect. The expression does not involve finding the sum of [tex]\(\frac{1}{4}\)[/tex] and 8.
- Statement 3: "Add 3 to the product of [tex]\(\frac{1}{4}\)[/tex] and 8 , then divide by 5"
- This is correct. It correctly describes the operations performed: first finding the product of [tex]\(\frac{1}{4}\)[/tex] and 8, then adding 3, followed by dividing by 5.
- Statement 4: "[tex]\(\frac{1}{4}\)[/tex] times the product of 8 and 3 , then divide by 5"
- This is incorrect. The expression does not involve multiplying [tex]\(\frac{1}{4}\)[/tex] by the product of 8 and 3.
Therefore, the correct statement that describes the expression [tex]\(\left(\frac{1}{4} \times 8 + 3\right) \div 5\)[/tex] is:
[tex]\[ \text{Add 3 to the product of } \frac{1}{4} \text{ and 8, then divide by 5} \][/tex]
