Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Let's tackle the problem step-by-step for each pair of numbers separately.
### Part (i): Insert six rational numbers between [tex]\(-\frac{1}{4}\)[/tex] and [tex]\(-\frac{2}{5}\)[/tex]
We need to find six rational numbers that lie between [tex]\(-\frac{1}{4}\)[/tex] and [tex]\(-\frac{2}{5}\)[/tex]. First, let's convert these fractions to decimal form for simplicity:
[tex]\[ -\frac{1}{4} = -0.25 \][/tex]
[tex]\[ -\frac{2}{5} = -0.4 \][/tex]
Now, we need to insert six rational numbers evenly spaced between these two values.
The resulting rational numbers between [tex]\(-0.25\)[/tex] and [tex]\(-0.4\)[/tex] are:
[tex]\[ -0.2714285714285714, -0.2928571428571428, -0.31428571428571433, -0.33571428571428574, -0.35714285714285715, -0.3785714285714286 \][/tex]
### Part (ii): Insert six rational numbers between [tex]\(\frac{21}{12}\)[/tex] and [tex]\(\frac{12}{21}\)[/tex]
We need to find six rational numbers that lie between [tex]\(\frac{21}{12}\)[/tex] and [tex]\(\frac{12}{21}\)[/tex]. First, let's convert these fractions to decimal form for simplicity:
[tex]\[ \frac{21}{12} \approx 1.75 \][/tex]
[tex]\[ \frac{12}{21} \approx 0.5714285714285714 \][/tex]
Now, we need to insert six rational numbers evenly spaced between these two values.
The resulting rational numbers between [tex]\(1.75\)[/tex] and [tex]\(0.5714285714285714\)[/tex] are:
[tex]\[ 1.5816326530612244, 1.413265306122449, 1.2448979591836733, 1.0765306122448979, 0.9081632653061223, 0.7397959183673469 \][/tex]
### Summary:
Six rational numbers between [tex]\(-\frac{1}{4}\)[/tex] and [tex]\(-\frac{2}{5}\)[/tex]:
[tex]\[ -0.2714285714285714, -0.2928571428571428, -0.31428571428571433, -0.33571428571428574, -0.35714285714285715, -0.3785714285714286 \][/tex]
Six rational numbers between [tex]\(\frac{21}{12}\)[/tex] and [tex]\(\frac{12}{21}\)[/tex]:
[tex]\[ 1.5816326530612244, 1.413265306122449, 1.2448979591836733, 1.0765306122448979, 0.9081632653061223, 0.7397959183673469 \][/tex]
By carefully calculating and inserting these rational numbers, we ensure that they lie evenly between the given pairs.
### Part (i): Insert six rational numbers between [tex]\(-\frac{1}{4}\)[/tex] and [tex]\(-\frac{2}{5}\)[/tex]
We need to find six rational numbers that lie between [tex]\(-\frac{1}{4}\)[/tex] and [tex]\(-\frac{2}{5}\)[/tex]. First, let's convert these fractions to decimal form for simplicity:
[tex]\[ -\frac{1}{4} = -0.25 \][/tex]
[tex]\[ -\frac{2}{5} = -0.4 \][/tex]
Now, we need to insert six rational numbers evenly spaced between these two values.
The resulting rational numbers between [tex]\(-0.25\)[/tex] and [tex]\(-0.4\)[/tex] are:
[tex]\[ -0.2714285714285714, -0.2928571428571428, -0.31428571428571433, -0.33571428571428574, -0.35714285714285715, -0.3785714285714286 \][/tex]
### Part (ii): Insert six rational numbers between [tex]\(\frac{21}{12}\)[/tex] and [tex]\(\frac{12}{21}\)[/tex]
We need to find six rational numbers that lie between [tex]\(\frac{21}{12}\)[/tex] and [tex]\(\frac{12}{21}\)[/tex]. First, let's convert these fractions to decimal form for simplicity:
[tex]\[ \frac{21}{12} \approx 1.75 \][/tex]
[tex]\[ \frac{12}{21} \approx 0.5714285714285714 \][/tex]
Now, we need to insert six rational numbers evenly spaced between these two values.
The resulting rational numbers between [tex]\(1.75\)[/tex] and [tex]\(0.5714285714285714\)[/tex] are:
[tex]\[ 1.5816326530612244, 1.413265306122449, 1.2448979591836733, 1.0765306122448979, 0.9081632653061223, 0.7397959183673469 \][/tex]
### Summary:
Six rational numbers between [tex]\(-\frac{1}{4}\)[/tex] and [tex]\(-\frac{2}{5}\)[/tex]:
[tex]\[ -0.2714285714285714, -0.2928571428571428, -0.31428571428571433, -0.33571428571428574, -0.35714285714285715, -0.3785714285714286 \][/tex]
Six rational numbers between [tex]\(\frac{21}{12}\)[/tex] and [tex]\(\frac{12}{21}\)[/tex]:
[tex]\[ 1.5816326530612244, 1.413265306122449, 1.2448979591836733, 1.0765306122448979, 0.9081632653061223, 0.7397959183673469 \][/tex]
By carefully calculating and inserting these rational numbers, we ensure that they lie evenly between the given pairs.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
