To solve the problem of determining the number by which we should multiply [tex]\(\frac{2}{7}\)[/tex] to get [tex]\(\frac{2}{15}\)[/tex], we need to set up an equation and solve for the unknown multiplier.
Let's denote the unknown multiplier by [tex]\(x\)[/tex].
We have:
[tex]\[
\frac{2}{7} \times x = \frac{2}{15}
\][/tex]
To isolate [tex]\(x\)[/tex], we can divide both sides of the equation by [tex]\(\frac{2}{7}\)[/tex]:
[tex]\[
x = \frac{\frac{2}{15}}{\frac{2}{7}}
\][/tex]
When dividing by a fraction, we multiply by its reciprocal. Thus, we get:
[tex]\[
x = \frac{2}{15} \times \frac{7}{2}
\][/tex]
Now, let's perform the multiplication:
[tex]\[
x = \left(\frac{2 \times 7}{15 \times 2}\right) = \frac{14}{30}
\][/tex]
We can simplify [tex]\(\frac{14}{30}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{14}{30} = \frac{14 \div 2}{30 \div 2} = \frac{7}{15}
\][/tex]
Thus, the number by which we should multiply [tex]\(\frac{2}{7}\)[/tex] to get [tex]\(\frac{2}{15}\)[/tex] is [tex]\(\frac{7}{15}\)[/tex], which is approximately [tex]\(0.4666666666666667\)[/tex].
