Mabrey connects 3 pieces of clay end to end that are each 34inch long. How many 316-inch pieces of clay can Mabrey cut?

To solve the problem, we need to determine how many \( \frac{3}{16} \)-inch pieces of clay Mabrey can cut from the total length of the clay.

### Step 1: Calculate the total length of the clay.
Mabrey connects 3 pieces of clay, each 34 inches long:

\[
\text{Total length} = 3 \times 34 = 102 \text{ inches}
\]

### Step 2: Determine how many \( \frac{3}{16} \)-inch pieces can be cut from 102 inches.
To find this, we divide the total length by the length of each piece:

\[
\text{Number of pieces} = \frac{102}{\frac{3}{16}} = 102 \times \frac{16}{3}
\]

### Step 3: Perform the multiplication.
\[
102 \times \frac{16}{3} = \frac{1632}{3} = 544 \text{ pieces}
\]

So, Mabrey can cut **544** pieces of \( \frac{3}{16} \)-inch clay.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How would the answer change if each piece of clay was 40 inches long instead of 34 inches?
2. What if Mabrey wanted to cut \( \frac{5}{16} \)-inch pieces instead?
3. How many \( \frac{1}{8} \)-inch pieces could Mabrey cut from the same length of clay?
4. What if the total length of the clay was 120 inches?
5. If Mabrey had only 2 pieces of clay, each 34 inches long, how many \( \frac{3}{16} \)-inch pieces could she cut?

**Tip:** When dealing with fractional units, converting the fraction to a decimal can sometimes make the math easier to handle!

Learn how to calculate how many 3/16-inch pieces of clay Mabrey can cut from three 34-inch pieces of clay. This problem involves fractional arithmetic and division of fractions, suitable for Grades 5-6.

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