Answer :
To determine whose ribbon is shorter, we know that a part of Zara's ribbon and a part of Sofia's ribbon are equal in length. Specifically, [tex]\(7 \frac{1}{4}\)[/tex] of Zara's ribbon is the same as [tex]\(\frac{1}{3}\)[/tex] of Sofia's ribbon.
Let's break it down step-by-step:
1. Convert the Mixed Number:
- [tex]\(7 \frac{1}{4}\)[/tex] is a mixed number. Converting it to an improper fraction:
[tex]\[
7 \frac{1}{4} = 7 + \frac{1}{4} = \frac{28}{4} + \frac{1}{4} = \frac{29}{4}
\][/tex]
2. Set up the Equation:
- We are given that:
[tex]\[
\frac{29}{4} \text{ of Zara's ribbon} = \frac{1}{3} \text{ of Sofia's ribbon}
\][/tex]
3. Determine Ribbon Lengths:
- If [tex]\(\frac{29}{4}\)[/tex] of Zara's ribbon equals [tex]\(\frac{1}{3}\)[/tex] of Sofia's ribbon, then:
[tex]\[
\frac{\text{Zara's ribbon length}}{29/4} = \frac{\text{Sofia's ribbon length}}{1/3}
\][/tex]
4. Calculate the Missing Parts:
- To find whose ribbon is shorter, compare the parts that are left of each ribbon.
5. Comparison:
- Zara's ribbon contributes less, meaning her ribbon has a larger fraction of the whole compared to Sofia's equal length. Thus, since a larger fraction equals a smaller whole, Zara’s ribbon is shorter.
Therefore, Zara's ribbon is shorter.
Let's break it down step-by-step:
1. Convert the Mixed Number:
- [tex]\(7 \frac{1}{4}\)[/tex] is a mixed number. Converting it to an improper fraction:
[tex]\[
7 \frac{1}{4} = 7 + \frac{1}{4} = \frac{28}{4} + \frac{1}{4} = \frac{29}{4}
\][/tex]
2. Set up the Equation:
- We are given that:
[tex]\[
\frac{29}{4} \text{ of Zara's ribbon} = \frac{1}{3} \text{ of Sofia's ribbon}
\][/tex]
3. Determine Ribbon Lengths:
- If [tex]\(\frac{29}{4}\)[/tex] of Zara's ribbon equals [tex]\(\frac{1}{3}\)[/tex] of Sofia's ribbon, then:
[tex]\[
\frac{\text{Zara's ribbon length}}{29/4} = \frac{\text{Sofia's ribbon length}}{1/3}
\][/tex]
4. Calculate the Missing Parts:
- To find whose ribbon is shorter, compare the parts that are left of each ribbon.
5. Comparison:
- Zara's ribbon contributes less, meaning her ribbon has a larger fraction of the whole compared to Sofia's equal length. Thus, since a larger fraction equals a smaller whole, Zara’s ribbon is shorter.
Therefore, Zara's ribbon is shorter.
