Answer:
To find the number by which \(-\frac{3}{13}\) should be multiplied so that the product is 24, we set up the equation:
\[
x \cdot \left(-\frac{3}{13}\right) = 24
\]
where \(x\) is the unknown number we need to find.
First, solve for \(x\) by multiplying both sides by \(-\frac{13}{3}\) (the reciprocal of \(-\frac{3}{13}\)) to isolate \(x\):
\[
x = 24 \cdot \left(-\frac{13}{3}\right)
\]
Calculate the right-hand side:
\[
x = 24 \cdot \left(-\frac{13}{3}\right) = 24 \cdot (-\frac{13}{3}) = -8 \cdot 13 = -104
\]
Therefore, the number by which \(-\frac{3}{13}\) should be multiplied so that the product is 24 is \(\boxed{-104}\).
Step-by-step explanation:
the answer is ➖ 104
To find the number by which we should multiply \(-\frac{3}{13}\) so that the product is 24, let's denote this number as \( x \).
We set up the equation based on the given condition:
\[ x \cdot \left(-\frac{3}{13}\right) = 24 \]
To solve for \( x \), multiply both sides by \(-\frac{13}{3}\) (the reciprocal of \(-\frac{3}{13}\)):
\[ x \cdot \left(-\frac{3}{13}\right) \cdot \left(-\frac{13}{3}\right) = 24 \cdot \left(-\frac{13}{3}\right) \]
Simplify the left-hand side:
\[ x = 24 \cdot \left(-\frac{13}{3}\right) \]
Calculate the multiplication on the right-hand side:
\[ x = -104 \]
Therefore, the number by which we should multiply \(-\frac{3}{13}\) so that the product is 24 is \(-104\).
