Question

2 tom used \\(\frac{3}{8}\\) of a piece of ribbon for a kite tail. from the remaining \\(\frac{5}{8}\\) of the ribbon, he cut pieces to tie weights on the kite tail. each tie was \\(\frac{1}{12}\\) of the whole ribbon. how many ties did he cut? how much ribbon was left over?

Explanation:

Step1: Find remaining ribbon fraction

Remaining ribbon: $\frac{5}{8}$ of the whole

Step2: Calculate number of ties

Divide remaining by per-tie fraction:
$$\frac{5}{8} \div \frac{1}{12} = \frac{5}{8} \times 12 = \frac{60}{8} = 7.5$$
Since we can only cut whole ties, we take the integer part: 7 ties.

Step3: Calculate used ribbon for ties

Total used for ties: $7 \times \frac{1}{12} = \frac{7}{12}$

Step4: Calculate leftover ribbon

Subtract used ties from remaining:
$$\frac{5}{8} - \frac{7}{12} = \frac{15}{24} - \frac{14}{24} = \frac{1}{24}$$

Answer:

He cut 7 ties. The leftover ribbon is $\frac{1}{24}$ of the whole ribbon.