Question
Gary has a box of pencils. In the box,
of the pencils have been sharpened. Select the three fractions that are proportional to the fraction of sharpened pencils in Gary’s box.
A
13\frac{1}{3}
3
1
B
17\frac{1}{7}
7
1
C
124\frac{12}{4}
4
12
D
1339\frac{13}{39}
39
13
E
1442\frac{14}{42}
42
14
F
217\frac{21}{7}
7
21
Answers
GPT-4o mini
To determine which fractions are proportional to the fraction of sharpened pencils in Gary's box, you need to find the simplest form or ratio that matches the fraction of sharpened pencils.
Unfortunately, you have not provided the fraction of sharpened pencils in the box, so I'll guide you through how to check for proportionality.
1. **Finding the fraction**: The fraction of sharpened pencils will typically be represented as \( \frac{x}{y} \), where \( x \) is the number of sharpened pencils, and \( y \) is the total number of pencils.
2. **Proportionality Check**: Two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \) are proportional if the cross-products are equal:
- \( a \times d = b \times c \)
3. **Checking Options**: Once you compute the fractional equivalent for different options, you'll be able to conduct the cross multiplication or simplify it down to its simplest form.
Assuming \( \frac{x}{y} \) is the fraction of sharpened pencils, you would follow through the possibilities (A through F), convert each mixed number to an improper fraction, and check if they match.
Let’s illustrate the approach with one example, say the fraction of sharpened pencils is \( \frac{1}{3} \):
- \( A: 13\frac{1}{3} = \frac{40}{3}, \ 3 = \frac{9}{3}, \ 1 = \frac{3}{3} \)
- Checking Proportions:
- \(40 \times 3\) vs \(9 \times 1\) does not equal; not proportional.
You would repeat this for all the given options and compare against your initial fraction.
Since you need to identify the correct options, ensure you list the correct original fraction that's representative of sharpened pencils for comparison.
Without knowing the original fraction of the sharpened pencils, I cannot definitively answer which options are proportional to it. Please provide that fraction, and I'll assist you further!
Unfortunately, you have not provided the fraction of sharpened pencils in the box, so I'll guide you through how to check for proportionality.
1. **Finding the fraction**: The fraction of sharpened pencils will typically be represented as \( \frac{x}{y} \), where \( x \) is the number of sharpened pencils, and \( y \) is the total number of pencils.
2. **Proportionality Check**: Two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \) are proportional if the cross-products are equal:
- \( a \times d = b \times c \)
3. **Checking Options**: Once you compute the fractional equivalent for different options, you'll be able to conduct the cross multiplication or simplify it down to its simplest form.
Assuming \( \frac{x}{y} \) is the fraction of sharpened pencils, you would follow through the possibilities (A through F), convert each mixed number to an improper fraction, and check if they match.
Let’s illustrate the approach with one example, say the fraction of sharpened pencils is \( \frac{1}{3} \):
- \( A: 13\frac{1}{3} = \frac{40}{3}, \ 3 = \frac{9}{3}, \ 1 = \frac{3}{3} \)
- Checking Proportions:
- \(40 \times 3\) vs \(9 \times 1\) does not equal; not proportional.
You would repeat this for all the given options and compare against your initial fraction.
Since you need to identify the correct options, ensure you list the correct original fraction that's representative of sharpened pencils for comparison.
Without knowing the original fraction of the sharpened pencils, I cannot definitively answer which options are proportional to it. Please provide that fraction, and I'll assist you further!