Mabrey connects 3 pieces of clay end to end that are each 3/4 inch long. How many 3/16 inch pieces of clay can Mabrey cut?

First, let's determine the total length of clay Mabrey has. Each piece of clay is \( \frac{3}{4} \) inch long, and Mabrey connects 3 pieces end to end:

\[
\text{Total length of clay} = 3 \times \frac{3}{4} = \frac{9}{4} \text{ inches}.
\]

Now, Mabrey wants to cut this total length into pieces that are each \( \frac{3}{16} \) inch long. To find out how many \( \frac{3}{16} \) inch pieces can be cut from \( \frac{9}{4} \) inches, we divide the total length by the length of each piece:

\[
\text{Number of pieces} = \frac{\frac{9}{4}}{\frac{3}{16}}.
\]

Dividing fractions involves multiplying by the reciprocal of the divisor:

\[
\frac{\frac{9}{4}}{\frac{3}{16}} = \frac{9}{4} \times \frac{16}{3} = \frac{9 \times 16}{4 \times 3} = \frac{144}{12} = 12.
\]

So, Mabrey can cut **12 pieces** of clay that are each \( \frac{3}{16} \) inch long.

Would you like more details on any part of this process, or do you have any further questions?

Here are some related questions to expand on this:

1. If each clay piece was \( \frac{5}{8} \) inch long instead, how many \( \frac{3}{16} \) inch pieces could Mabrey cut?
2. What would be the total length of 12 pieces of \( \frac{3}{16} \) inch clay?
3. If Mabrey only had two pieces of \( \frac{3}{4} \) inch clay, how many \( \frac{3}{16} \) inch pieces could be cut?
4. How would the number of \( \frac{3}{16} \) inch pieces change if the total length of clay was increased by another \( \frac{3}{4} \) inch piece?
5. If the pieces were cut into \( \frac{1}{8} \) inch segments, how many could Mabrey cut from the total clay?

**Tip:** When working with fractions in division, always remember to multiply by the reciprocal to simplify the calculation!

Discover how many \( \frac{3}{16} \) inch pieces of clay Mabrey can cut from 3 pieces, each 3/4 inch long. Detailed step-by-step solution with fraction division explained. Suitable for students in Grades 5-6.

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