To find the rational numbers based on the given numerators and denominators, we will perform the division for each pair of numerator and denominator.
(i) Numerator = 3, Denominator = -7:
We perform the division:
[tex]\[ \frac{3}{-7} \][/tex]
This simplifies to:
[tex]\[ -0.42857142857142855 \][/tex]
So, the rational number for the given values is:
[tex]\[ -0.42857142857142855 \][/tex]
(ii) Denominator = -4, Numerator = -3:
We perform the division:
[tex]\[ \frac{-3}{-4} \][/tex]
Since dividing two negative numbers results in a positive number:
[tex]\[ 0.75 \][/tex]
So, the rational number for the given values is:
[tex]\[ 0.75 \][/tex]
(iii) Numerator = 15 - 7, Denominator = 13 - 6:
First, we calculate the numerator and denominator separately:
[tex]\[ 15 - 7 = 8 \][/tex]
[tex]\[ 13 - 6 = 7 \][/tex]
We then perform the division:
[tex]\[ \frac{8}{7} \][/tex]
Simplifying this, we get:
[tex]\[ 1.1428571428571428 \][/tex]
So, the rational number for the given values is:
[tex]\[ 1.1428571428571428 \][/tex]
(iv) Numerator = 7 + 6, Denominator = 17 \times (-2):
First, we calculate the numerator and denominator separately:
[tex]\[ 7 + 6 = 13 \][/tex]
[tex]\[ 17 \times (-2) = -34 \][/tex]
We then perform the division:
[tex]\[ \frac{13}{-34} \][/tex]
Simplifying this, we get:
[tex]\[ -0.38235294117647056 \][/tex]
So, the rational number for the given values is:
[tex]\[ -0.38235294117647056 \][/tex]
To summarize, the rational numbers are:
(i) [tex]\(-0.42857142857142855\)[/tex]
(ii) [tex]\(0.75\)[/tex]
(iii) [tex]\(1.1428571428571428\)[/tex]
(iv) [tex]\(-0.38235294117647056\)[/tex]
