College

3. Which statement describes the value of the expression below?

[tex]67 \times \frac{1}{6}[/tex]

A. The value is less than 67.
B. The value is equal to 67.
C. The value is greater than 67.
D. The value is greater than 0 and less than 1.

4. Which expression is equivalent to [tex]5 \times \frac{3}{4}[/tex]?

A. [tex]\frac{5}{1} + \frac{3}{4}[/tex]
B. [tex]\frac{5}{1} - \frac{3}{4}[/tex]
C. [tex]\frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4}[/tex]
D. [tex]\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4} \times \frac{3}{4} \times \frac{3}{4}[/tex]

7. A state fair held a heaviest-pumpkin contest. The winning pumpkin weighed 2,050 pounds. What is the weight, in ounces, of the winning pumpkin?

A. 8,200
B. 16,400
C. 24,600
D. 32,800

8. The line plot shows the number of bags of grapes, grouped by weight, to the nearest [tex]\frac{1}{8}[/tex] pound.

**Weight of Bags of Grapes**

- How many bags of grapes had a weight of [tex]\frac{3}{8}[/tex] pound or less?
- What was the total weight of the grapes in the bags that had a weight of [tex]\frac{3}{8}[/tex] pound or less?

Answer :

Sure! Let's solve each part of the question step by step.

### 3. Which statement describes the value of the expression [tex]\( 67 \times \frac{1}{6} \)[/tex]?

To solve this, we calculate the expression:
- Multiply 67 by [tex]\(\frac{1}{6}\)[/tex].
- This gives [tex]\( 67 \times \frac{1}{6} = \frac{67}{6} \)[/tex].

Now we know [tex]\(\frac{67}{6}\)[/tex] is a division operation, which will result in a value less than 67 because you are dividing 67 into 6 parts.

So, the statement that accurately describes this value is:
- A. The value is less than 67.

### 4. Which expression is equivalent to [tex]\( 5 \times \frac{3}{4} \)[/tex]?

To solve this, we consider the meaning of multiplication here:
- [tex]\(5 \times \frac{3}{4}\)[/tex] means we add [tex]\(\frac{3}{4}\)[/tex] five times.

This is equivalent to:
- [tex]\(\frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4}\)[/tex].

The equivalent expression is:
- C. [tex]\(\frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4} + \frac{3}{4}\)[/tex]

### 7. What is the weight, in ounces, of the winning pumpkin weighing 2,050 pounds?

To convert pounds to ounces:
- We use the conversion factor that 1 pound equals 16 ounces.
- Therefore, 2,050 pounds converted to ounces is [tex]\( 2,050 \times 16 \)[/tex].

This calculates to:
- D. 32,800 ounces.

### 8. How many bags of grapes had a weight of [tex]\(\frac{3}{8}\)[/tex] pound or less, and what was their total weight?

Assuming weights of bags in a dataset are provided, to find bags weighing [tex]\(\frac{3}{8}\)[/tex] pound or less:
- We list the weights and count those that are equal to or less than [tex]\(\frac{3}{8}\)[/tex].

For example, if the weights are [tex]\(\frac{1}{8}, \frac{1}{8}, \frac{1}{8}, \frac{2}{8}, \frac{2}{8}, \frac{3}{8}, \frac{3}{8}, \frac{3}{8}\)[/tex]:
- The bags that weigh [tex]\(\frac{3}{8}\)[/tex] pound or less are all of them in the list above.

The number of such bags:
- 8 bags.

Their total weight is the sum of these individual weights:
- 2.0 pounds.

These step-by-step results give us a clear understanding of each part of the question.