Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To express the rational number [tex]\(\frac{-5}{6}\)[/tex] with a given numerator, we need to find the corresponding denominator for each case. The general approach is to set up a proportion that ensures the new fraction is equivalent to the original fraction.
### Part (a)
Given numerator: [tex]\(35\)[/tex]
Let's set up the proportion to find the denominator:
[tex]\[ \frac{-5}{6} = \frac{35}{d_a} \][/tex]
We solve for [tex]\(d_a\)[/tex] by cross-multiplying:
[tex]\[ -5 \times d_a = 35 \times 6 \][/tex]
So,
[tex]\[ -5d_a = 210 \][/tex]
Next, solve for [tex]\(d_a\)[/tex]:
[tex]\[ d_a = \frac{210}{-5} = -42 \][/tex]
Therefore, the rational number [tex]\(\frac{-5}{6}\)[/tex] with numerator 35 is [tex]\(\frac{35}{-42}\)[/tex].
### Part (b)
Given numerator: [tex]\(-110\)[/tex]
Let's set up the proportion to find the denominator for this new numerator:
[tex]\[ \frac{-5}{6} = \frac{-110}{d_b} \][/tex]
We solve for [tex]\(d_b\)[/tex] by cross-multiplying:
[tex]\[ -5 \times d_b = -110 \times 6 \][/tex]
So,
[tex]\[ -5d_b = -660 \][/tex]
Next, solve for [tex]\(d_b\)[/tex]:
[tex]\[ d_b = \frac{-660}{-5} = 132 \][/tex]
Therefore, the rational number [tex]\(\frac{-5}{6}\)[/tex] with numerator [tex]\(-110\)[/tex] is [tex]\(\frac{-110}{132}\)[/tex].
### Summary
- For numerator 35, the fraction is [tex]\(\frac{35}{-42}\)[/tex].
- For numerator [tex]\(-110\)[/tex], the fraction is [tex]\(\frac{-110}{132}\)[/tex].
### Part (a)
Given numerator: [tex]\(35\)[/tex]
Let's set up the proportion to find the denominator:
[tex]\[ \frac{-5}{6} = \frac{35}{d_a} \][/tex]
We solve for [tex]\(d_a\)[/tex] by cross-multiplying:
[tex]\[ -5 \times d_a = 35 \times 6 \][/tex]
So,
[tex]\[ -5d_a = 210 \][/tex]
Next, solve for [tex]\(d_a\)[/tex]:
[tex]\[ d_a = \frac{210}{-5} = -42 \][/tex]
Therefore, the rational number [tex]\(\frac{-5}{6}\)[/tex] with numerator 35 is [tex]\(\frac{35}{-42}\)[/tex].
### Part (b)
Given numerator: [tex]\(-110\)[/tex]
Let's set up the proportion to find the denominator for this new numerator:
[tex]\[ \frac{-5}{6} = \frac{-110}{d_b} \][/tex]
We solve for [tex]\(d_b\)[/tex] by cross-multiplying:
[tex]\[ -5 \times d_b = -110 \times 6 \][/tex]
So,
[tex]\[ -5d_b = -660 \][/tex]
Next, solve for [tex]\(d_b\)[/tex]:
[tex]\[ d_b = \frac{-660}{-5} = 132 \][/tex]
Therefore, the rational number [tex]\(\frac{-5}{6}\)[/tex] with numerator [tex]\(-110\)[/tex] is [tex]\(\frac{-110}{132}\)[/tex].
### Summary
- For numerator 35, the fraction is [tex]\(\frac{35}{-42}\)[/tex].
- For numerator [tex]\(-110\)[/tex], the fraction is [tex]\(\frac{-110}{132}\)[/tex].
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.