Let's go through each question step-by-step to find the correct answers.
### Question 1:
1. What is the product of the largest and the smallest fraction from the following list? [tex]\(\frac{9}{11}, \frac{3}{11}, \frac{7}{11}, \frac{5}{11}, \frac{10}{11}, \frac{6}{11}\)[/tex]
To solve this, we need to identify the largest and smallest fractions from the list and then calculate their product.
- The smallest fraction is [tex]\(\frac{3}{11}\)[/tex].
- The largest fraction is [tex]\(\frac{10}{11}\)[/tex].
Now, find the product of these two fractions:
[tex]\[
\frac{3}{11} \times \frac{10}{11} = \frac{3 \times 10}{11 \times 11} = \frac{30}{121}
\][/tex]
Thus, the correct option is:
b. [tex]\(\frac{30}{121}\)[/tex]
### Question 2:
2. Which option describes how the decimal point in 8.3127 should be shifted when it is divided by:
The problem statement does not specify the divisor, but there is usually an implied standard instruction in mathematical problems like this unless specifically stated otherwise. When dividing by 100 (which is the usual context):
- When you divide by 100, you move the decimal point 2 places to the left.
Therefore, the correct option is:
a. 2 places to the left
### Question 3:
3. The steps a student takes to solve a problem are described below.
- Step 1: Creates 3 squares.
- Step 2: Divides each square into 4 equal parts.
- Step 3: Shades 2 squares completely and half of the third square.
- Step 4: Reports the total number of shaded parts as answer.
Let’s interpret the steps:
- Step 1: 3 squares.
- Step 2: Each square into 4 equal parts means each square has 4 parts, so 3 squares give [tex]\(3 \times 4 = 12\)[/tex] total parts.
- Step 3: Shades 2 squares completely. This means [tex]\(2 \text{ squares} \times 4 \text{ parts per square} = 8 \text{ parts}\)[/tex]. Additionally, half of the third square means [tex]\(0.5 \times 4 = 2\)[/tex] parts.
- Step 4: Total shaded parts: [tex]\(8+2 = 10\)[/tex].
Given that the student shades parts and counts them, the problem could be about finding the fraction or portion.
A reasonable problem the student could be solving might be:
“What fraction of the total parts is shaded if 2 full squares and half of another square out of 3 squares (each divided into 4 parts) are shaded?”
The answer total can be summarized as identifying how many parts are shaded out of the total possible parts in a visual fraction problem.
