Certainly! Let's solve the equation \( d = \frac{m}{v} \) for mass, \( m \).
1. Understanding the relationship: The equation \( d = \frac{m}{v} \) tells us that density (\( d \)) is equal to mass (\( m \)) divided by volume (\( v \)).
2. Objective: We need to solve for the mass (\( m \)). This means we need to isolate \( m \) on one side of the equation.
3. Isolate mass (\( m \)):
- Start with the given equation:
[tex]\[
d = \frac{m}{v}
\][/tex]
- To isolate \( m \), we need to eliminate the division by \( v \). We can do this by multiplying both sides of the equation by \( v \):
[tex]\[
d \cdot v = \left(\frac{m}{v}\right) \cdot v
\][/tex]
4. Simplify the equation:
- When we multiply \( \frac{m}{v} \) by \( v \), the \( v \) terms on the right-hand side cancel out, leaving us with:
[tex]\[
d \cdot v = m
\][/tex]
5. Final solution: The equation simplifies to:
[tex]\[
m = d \cdot v
\][/tex]
Therefore, the mass (\( m \)) is equal to the product of the density (\( d \)) and the volume (\( v \)).
So, the solution to the equation \( d = \frac{m}{v} \) for mass (\( m \)) is:
[tex]\[
m = d \cdot v
\][/tex]
