Sure! Let's solve each part step-by-step by identifying rational numbers that fall within the given ranges.
### 1. Write 10 rational numbers between -7 and -4
We need to identify 10 rational numbers between -7 and -4. Here are some possible choices in ascending order:
- -6.9
- -6.8
- -6.7
- -6.6
- -6.5
- -6.4
- -6.3
- -6.2
- -6.1
- -6.0
### 2. Write 5 rational numbers between [tex]\(\frac{5}{7}\)[/tex] and [tex]\(\frac{7}{9}\)[/tex]
First, let's convert [tex]\(\frac{5}{7}\)[/tex] and [tex]\(\frac{7}{9}\)[/tex] into decimal form to understand the range better.
[tex]\[
\frac{5}{7} \approx 0.714
\][/tex]
[tex]\[
\frac{7}{9} \approx 0.778
\][/tex]
Now, let's identify 5 rational numbers within this range:
- 0.72
- 0.73
- 0.74
- 0.75
- 0.76
### 3. Write 5 rational numbers between [tex]\(\frac{-3}{8}\)[/tex] and [tex]\(\frac{-5}{9}\)[/tex]
Again, let's convert [tex]\(\frac{-3}{8}\)[/tex] and [tex]\(\frac{-5}{9}\)[/tex] into decimal form.
[tex]\[
\frac{-3}{8} = -0.375
\][/tex]
[tex]\[
\frac{-5}{9} \approx -0.556
\][/tex]
Now, we can select 5 rational numbers within this range:
- -0.38
- -0.40
- -0.42
- -0.44
- -0.46
Hence, the solutions are:
- 10 rational numbers between -7 and -4: -6.9, -6.8, -6.7, -6.6, -6.5, -6.4, -6.3, -6.2, -6.1, -6.0
- 5 rational numbers between [tex]\(\frac{5}{7}\)[/tex] and [tex]\(\frac{7}{9}\)[/tex]: 0.72, 0.73, 0.74, 0.75, 0.76
- 5 rational numbers between [tex]\(\frac{-3}{8}\)[/tex] and [tex]\(\frac{-5}{9}\)[/tex]: -0.38, -0.40, -0.42, -0.44, -0.46
