13. Insert six rational numbers between:

(i) [tex]$-\frac{1}{4}$[/tex] and [tex]$-\frac{2}{5}$[/tex]

(ii) [tex]$\frac{21}{12}$[/tex] and [tex]$\frac{12}{21}$[/tex]

Question

25-06-2024
Mathematics

Answered

13. Insert six rational numbers between:

(i) [tex]$-\frac{1}{4}$[/tex] and [tex]$-\frac{2}{5}$[/tex]

(ii) [tex]$\frac{21}{12}$[/tex] and [tex]$\frac{12}{21}$[/tex]

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-25T05:07:50-04:00

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.

13. Insert six rational numbers between:(i) [tex]\(-\frac{1}{4}\)[/tex] and [tex]\(-\frac{2}{5}\)[/tex](ii) [tex]\(\frac{21}{12}\)[/tex] and [tex]\(\frac{12}{21}\)[/tex]

Answer :

Other Questions

13. Insert six rational numbers between:

(i) [tex]\(-\frac{1}{4}\)[/tex] and [tex]\(-\frac{2}{5}\)[/tex]

(ii) [tex]\(\frac{21}{12}\)[/tex] and [tex]\(\frac{12}{21}\)[/tex]