To determine how many pieces can be made from a chain of 35 cm in length, with each piece having a length of [tex]\(\frac{5}{7}\)[/tex] cm, follow these steps:
1. Understand the Problem:
We need to find how many smaller pieces, each of length [tex]\(\frac{5}{7}\)[/tex] cm, can be obtained from a single chain of length 35 cm.
2. Set up the Division:
To find the number of pieces, we need to divide the total length of the chain by the length of each piece. This is expressed as:
[tex]\[
\text{Number of pieces} = \frac{\text{Total length of the chain}}{\text{Length of each piece}}
\][/tex]
3. Substitute the values:
Here, the total length of the chain is 35 cm, and the length of each piece is [tex]\(\frac{5}{7}\)[/tex] cm. So, we can write:
[tex]\[
\text{Number of pieces} = \frac{35}{\frac{5}{7}}
\][/tex]
4. Simplify the Division:
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\(\frac{5}{7}\)[/tex] is [tex]\(\frac{7}{5}\)[/tex]. Therefore:
[tex]\[
\frac{35}{\frac{5}{7}} = 35 \times \frac{7}{5}
\][/tex]
5. Perform the Multiplication:
Multiply 35 by [tex]\(\frac{7}{5}\)[/tex]:
[tex]\[
35 \times \frac{7}{5} = 35 \div 5 \times 7 = 7 \times 7 = 49
\][/tex]
6. Conclusion:
Thus, the number of pieces that can be made from the 35 cm long chain, with each piece being [tex]\(\frac{5}{7}\)[/tex] cm in length, is 49.
Therefore, 49 pieces can be made from the chain.
