Answer :
We start with the equation
[tex]$$
\frac{-\frac{12}{18}}{x} = \frac{14}{15}.
$$[/tex]
Step 1. Multiply both sides by [tex]$x$[/tex] to isolate the fraction on the left:
[tex]$$
-\frac{12}{18} = \frac{14}{15}\, x.
$$[/tex]
Step 2. To solve for [tex]$x$[/tex], divide both sides by [tex]$\frac{14}{15}$[/tex]:
[tex]$$
x = \frac{-\frac{12}{18}}{\frac{14}{15}}.
$$[/tex]
Step 3. Simplify the fraction [tex]$-\frac{12}{18}$[/tex] by dividing numerator and denominator by 6:
[tex]$$
-\frac{12}{18} = -\frac{2}{3}.
$$[/tex]
Step 4. Substitute the simplified fraction into the expression for [tex]$x$[/tex]:
[tex]$$
x = \frac{-\frac{2}{3}}{\frac{14}{15}}.
$$[/tex]
Step 5. Dividing by a fraction is the same as multiplying by its reciprocal, so
[tex]$$
x = -\frac{2}{3} \times \frac{15}{14}.
$$[/tex]
Step 6. Multiply the fractions:
[tex]$$
x = -\frac{2 \times 15}{3 \times 14} = -\frac{30}{42}.
$$[/tex]
Step 7. Simplify the fraction [tex]$\frac{30}{42}$[/tex] by dividing numerator and denominator by 6:
[tex]$$
-\frac{30}{42} = -\frac{5}{7}.
$$[/tex]
So, the number by which [tex]$-\frac{12}{18}$[/tex] must be divided to get [tex]$\frac{14}{15}$[/tex] is
[tex]$$
\boxed{-\frac{5}{7}}.
$$[/tex]
This value is approximately [tex]$-0.7142857$[/tex].
[tex]$$
\frac{-\frac{12}{18}}{x} = \frac{14}{15}.
$$[/tex]
Step 1. Multiply both sides by [tex]$x$[/tex] to isolate the fraction on the left:
[tex]$$
-\frac{12}{18} = \frac{14}{15}\, x.
$$[/tex]
Step 2. To solve for [tex]$x$[/tex], divide both sides by [tex]$\frac{14}{15}$[/tex]:
[tex]$$
x = \frac{-\frac{12}{18}}{\frac{14}{15}}.
$$[/tex]
Step 3. Simplify the fraction [tex]$-\frac{12}{18}$[/tex] by dividing numerator and denominator by 6:
[tex]$$
-\frac{12}{18} = -\frac{2}{3}.
$$[/tex]
Step 4. Substitute the simplified fraction into the expression for [tex]$x$[/tex]:
[tex]$$
x = \frac{-\frac{2}{3}}{\frac{14}{15}}.
$$[/tex]
Step 5. Dividing by a fraction is the same as multiplying by its reciprocal, so
[tex]$$
x = -\frac{2}{3} \times \frac{15}{14}.
$$[/tex]
Step 6. Multiply the fractions:
[tex]$$
x = -\frac{2 \times 15}{3 \times 14} = -\frac{30}{42}.
$$[/tex]
Step 7. Simplify the fraction [tex]$\frac{30}{42}$[/tex] by dividing numerator and denominator by 6:
[tex]$$
-\frac{30}{42} = -\frac{5}{7}.
$$[/tex]
So, the number by which [tex]$-\frac{12}{18}$[/tex] must be divided to get [tex]$\frac{14}{15}$[/tex] is
[tex]$$
\boxed{-\frac{5}{7}}.
$$[/tex]
This value is approximately [tex]$-0.7142857$[/tex].
