Paula cut ribbon from a spool for a craft project. Each piece of ribbon changed the length of the ribbon remaining on the spool by [tex]-1.2[/tex] feet. When Paula finished, the length of ribbon on the spool had changed by [tex]-9 \frac{3}{5}[/tex] feet. How many pieces of ribbon did Paula cut?

Show your work.

Sure! Let's solve the problem step-by-step:

1. Understanding the Problem:
- Each piece of ribbon Paula cut from the spool reduces the length of the ribbon by 1.2 feet.
- The total change in the length of the ribbon on the spool is [tex]$-9 \frac{3}{5}$[/tex] feet.

2. Convert the Fraction to a Decimal:
- Before proceeding, convert the mixed number [tex]$-9 \frac{3}{5}$[/tex] to a decimal.
- The fractional part [tex]$\frac{3}{5}$[/tex] is equal to 0.6.
- So, [tex]$-9 \frac{3}{5}$[/tex] is equal to [tex]$-9.6$[/tex] feet.

3. Calculate the Number of Pieces:
- To find out how many pieces of ribbon Paula cut, divide the total change in length by the change in length per piece:
[tex]\[
\text{Number of pieces} = \frac{\text{Total change in ribbon}}{\text{Change per piece}} = \frac{-9.6}{-1.2}
\][/tex]

4. Perform the Division:
- Divide [tex]$-9.6$[/tex] by [tex]$-1.2$[/tex]:
[tex]\[
\frac{-9.6}{-1.2} = 8
\][/tex]

5. Conclusion:
- Paula cut 8 pieces of ribbon from the spool.

That's how you can determine the number of pieces Paula cut based on the change in ribbon length!