Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Let's solve the problem step-by-step:
First, we need to determine the decimal equivalents of [tex]\(-\frac{4}{5}\)[/tex] and [tex]\(-\frac{3}{7}\)[/tex] so that we can compare.
1. Convert [tex]\(-\frac{4}{5}\)[/tex] to decimal:
[tex]\[ -\frac{4}{5} = -0.8 \][/tex]
2. Convert [tex]\(-\frac{3}{7}\)[/tex] to decimal:
[tex]\[ -\frac{3}{7} \approx -0.4286 \][/tex]
We are looking for rational numbers (fractions) that lie between [tex]\(-0.8\)[/tex] and [tex]\(-0.4286\)[/tex]. Let's examine each option:
### Option (a): [tex]\(-\frac{29}{15}\)[/tex] and [tex]\(-\frac{20}{15}\)[/tex]
1. Convert [tex]\(-\frac{29}{15}\)[/tex] to decimal:
[tex]\[ -\frac{29}{15} \approx -1.9333 \][/tex]
2. Convert [tex]\(-\frac{20}{15}\)[/tex] to decimal:
[tex]\[ -\frac{20}{15} \approx -1.3333 \][/tex]
Both [tex]\(-1.9333\)[/tex] and [tex]\(-1.3333\)[/tex] are less than [tex]\(-0.8\)[/tex]. Thus, neither of these two numbers lie between [tex]\(-0.8\)[/tex] and [tex]\(-0.4286\)[/tex].
### Option (b): [tex]\(-\frac{21}{35}\)[/tex] and [tex]\(-\frac{20}{35}\)[/tex]
1. Convert [tex]\(-\frac{21}{35}\)[/tex] to decimal:
[tex]\[ -\frac{21}{35} = -0.6 \][/tex]
2. Convert [tex]\(-\frac{20}{35}\)[/tex] to decimal:
[tex]\[ -\frac{20}{35} \approx -0.5714 \][/tex]
Both [tex]\(-0.6\)[/tex] and [tex]\(-0.5714\)[/tex] are between [tex]\(-0.8\)[/tex] and [tex]\(-0.4286\)[/tex]. Hence, these numbers satisfy the condition.
### Option (c): [tex]\(-\frac{28}{35}\)[/tex] and [tex]\(-\frac{25}{35}\)[/tex]
1. Convert [tex]\(-\frac{28}{35}\)[/tex] to decimal:
[tex]\[ -\frac{28}{35} \approx -0.8 \][/tex]
2. Convert [tex]\(-\frac{25}{35}\)[/tex] to decimal:
[tex]\[ -\frac{25}{35} \approx -0.7143 \][/tex]
Neither of these numbers are within the range [tex]\(-0.8\)[/tex] and [tex]\(-0.4286\)[/tex]. While [tex]\(-0.7143\)[/tex] could be considered in range, [tex]\(-0.8\)[/tex] is the lower boundary and does not strictly satisfy lying between the values.
### Option (d): [tex]\(-\frac{14}{35}\)[/tex] and [tex]\(-\frac{13}{35}\)[/tex]
1. Convert [tex]\(-\frac{14}{35}\)[/tex] to decimal:
[tex]\[ -\frac{14}{35} \approx -0.4 \][/tex]
2. Convert [tex]\(-\frac{13}{35}\)[/tex] to decimal:
[tex]\[ -\frac{13}{35} \approx -0.3714 \][/tex]
Both [tex]\(-0.4\)[/tex] and [tex]\(-0.3714\)[/tex] are greater than [tex]\(-0.4286\)[/tex]. Thus, neither of these numbers satisfy the condition.
### Conclusion:
The rational numbers in option (b) are the ones that lie between [tex]\(-\frac{4}{5}\)[/tex] and [tex]\(-\frac{3}{7}\)[/tex]:
[tex]\(\boxed{b}\)[/tex]
First, we need to determine the decimal equivalents of [tex]\(-\frac{4}{5}\)[/tex] and [tex]\(-\frac{3}{7}\)[/tex] so that we can compare.
1. Convert [tex]\(-\frac{4}{5}\)[/tex] to decimal:
[tex]\[ -\frac{4}{5} = -0.8 \][/tex]
2. Convert [tex]\(-\frac{3}{7}\)[/tex] to decimal:
[tex]\[ -\frac{3}{7} \approx -0.4286 \][/tex]
We are looking for rational numbers (fractions) that lie between [tex]\(-0.8\)[/tex] and [tex]\(-0.4286\)[/tex]. Let's examine each option:
### Option (a): [tex]\(-\frac{29}{15}\)[/tex] and [tex]\(-\frac{20}{15}\)[/tex]
1. Convert [tex]\(-\frac{29}{15}\)[/tex] to decimal:
[tex]\[ -\frac{29}{15} \approx -1.9333 \][/tex]
2. Convert [tex]\(-\frac{20}{15}\)[/tex] to decimal:
[tex]\[ -\frac{20}{15} \approx -1.3333 \][/tex]
Both [tex]\(-1.9333\)[/tex] and [tex]\(-1.3333\)[/tex] are less than [tex]\(-0.8\)[/tex]. Thus, neither of these two numbers lie between [tex]\(-0.8\)[/tex] and [tex]\(-0.4286\)[/tex].
### Option (b): [tex]\(-\frac{21}{35}\)[/tex] and [tex]\(-\frac{20}{35}\)[/tex]
1. Convert [tex]\(-\frac{21}{35}\)[/tex] to decimal:
[tex]\[ -\frac{21}{35} = -0.6 \][/tex]
2. Convert [tex]\(-\frac{20}{35}\)[/tex] to decimal:
[tex]\[ -\frac{20}{35} \approx -0.5714 \][/tex]
Both [tex]\(-0.6\)[/tex] and [tex]\(-0.5714\)[/tex] are between [tex]\(-0.8\)[/tex] and [tex]\(-0.4286\)[/tex]. Hence, these numbers satisfy the condition.
### Option (c): [tex]\(-\frac{28}{35}\)[/tex] and [tex]\(-\frac{25}{35}\)[/tex]
1. Convert [tex]\(-\frac{28}{35}\)[/tex] to decimal:
[tex]\[ -\frac{28}{35} \approx -0.8 \][/tex]
2. Convert [tex]\(-\frac{25}{35}\)[/tex] to decimal:
[tex]\[ -\frac{25}{35} \approx -0.7143 \][/tex]
Neither of these numbers are within the range [tex]\(-0.8\)[/tex] and [tex]\(-0.4286\)[/tex]. While [tex]\(-0.7143\)[/tex] could be considered in range, [tex]\(-0.8\)[/tex] is the lower boundary and does not strictly satisfy lying between the values.
### Option (d): [tex]\(-\frac{14}{35}\)[/tex] and [tex]\(-\frac{13}{35}\)[/tex]
1. Convert [tex]\(-\frac{14}{35}\)[/tex] to decimal:
[tex]\[ -\frac{14}{35} \approx -0.4 \][/tex]
2. Convert [tex]\(-\frac{13}{35}\)[/tex] to decimal:
[tex]\[ -\frac{13}{35} \approx -0.3714 \][/tex]
Both [tex]\(-0.4\)[/tex] and [tex]\(-0.3714\)[/tex] are greater than [tex]\(-0.4286\)[/tex]. Thus, neither of these numbers satisfy the condition.
### Conclusion:
The rational numbers in option (b) are the ones that lie between [tex]\(-\frac{4}{5}\)[/tex] and [tex]\(-\frac{3}{7}\)[/tex]:
[tex]\(\boxed{b}\)[/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
