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Answer :
To solve the problem of determining the greatest number of bows Emily can make, let's go through the process step-by-step.
1. Understand the Problem:
- Emily has a ribbon that is 23 yards long.
- She needs [tex]\(1 \frac{5}{6}\)[/tex] yards of ribbon to make each bow.
2. Convert the Mixed Number to an Improper Fraction:
- [tex]\(1 \frac{5}{6}\)[/tex] can be expressed as an improper fraction. [tex]\(1 \frac{5}{6} = \frac{11}{6}\)[/tex].
3. Calculate the Total Length of Ribbon Required for One Bow:
- Each bow requires [tex]\(\frac{11}{6}\)[/tex] yards of ribbon.
4. Determine How Many Full Bows Can Be Made:
- We need to determine how many times the length of ribbon needed for one bow ([tex]\(\frac{11}{6}\)[/tex] yards) can fit into the total length of the ribbon (23 yards).
- To find this, divide the total ribbon (23 yards) by the ribbon needed per bow ([tex]\(\frac{11}{6}\)[/tex] yards).
- In fractional form, this division is:
[tex]\[
23 \div \frac{11}{6} = 23 \times \frac{6}{11} = \frac{138}{11} \approx 12.545
\][/tex]
- Since Emily cannot make a fraction of a bow, she can only make a whole number of bows. Thus, she can make 12 full bows.
Therefore, the greatest number of bows Emily can make is 12.
1. Understand the Problem:
- Emily has a ribbon that is 23 yards long.
- She needs [tex]\(1 \frac{5}{6}\)[/tex] yards of ribbon to make each bow.
2. Convert the Mixed Number to an Improper Fraction:
- [tex]\(1 \frac{5}{6}\)[/tex] can be expressed as an improper fraction. [tex]\(1 \frac{5}{6} = \frac{11}{6}\)[/tex].
3. Calculate the Total Length of Ribbon Required for One Bow:
- Each bow requires [tex]\(\frac{11}{6}\)[/tex] yards of ribbon.
4. Determine How Many Full Bows Can Be Made:
- We need to determine how many times the length of ribbon needed for one bow ([tex]\(\frac{11}{6}\)[/tex] yards) can fit into the total length of the ribbon (23 yards).
- To find this, divide the total ribbon (23 yards) by the ribbon needed per bow ([tex]\(\frac{11}{6}\)[/tex] yards).
- In fractional form, this division is:
[tex]\[
23 \div \frac{11}{6} = 23 \times \frac{6}{11} = \frac{138}{11} \approx 12.545
\][/tex]
- Since Emily cannot make a fraction of a bow, she can only make a whole number of bows. Thus, she can make 12 full bows.
Therefore, the greatest number of bows Emily can make is 12.
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