- Express the proportion as a fractional equation: \(\frac{0.45}{3} = \frac{x}{12}\).
- Multiply both sides by 12 to isolate the variable \(x\): \(x = \frac{0.45}{3} \times 12\).
- Calculate the division and multiplication: \(0.15 \times 12 = 1.8\).
- Final Answer: \(\boxed{1.8}\).
Explanation
- Analyzing the Proportion
The problem presents a proportion \(0.45 : 3 = x : 12\), where \(x\) is the unknown value we need to find. A proportion is a statement that two ratios are equal, which can be expressed in fractional form as \(\frac{a}{b} = \frac{c}{d}\). In this case, our proportion is \(\frac{0.45}{3} = \frac{x}{12}\). Our objective is to isolate \(x\) and calculate its numerical value.
- Solving for the Unknown Value x
To solve the equation \(\frac{0.45}{3} = \frac{x}{12}\), we need to isolate \(x\). We can do this by multiplying both sides of the equation by 12:
\[x = \frac{0.45}{3} \times 12\]
First, we simplify the ratio \(\frac{0.45}{3}\). Dividing \(0.45\) by \(3\) gives \(0.15\).
Now, we multiply \(0.15\) by \(12\):
\[x = 0.15 \times 12 = 1.8\]
Thus, the value of \(x\) is \(1.8\).
- Final Conclusion
We have determined that \(x = 1.8\). We can verify this by plugging the value back into the original proportion:
\(\frac{0.45}{3} = 0.15\)
\(\frac{1.8}{12} = 0.15\)
Since both sides equal \(0.15\), our solution is correct. The final answer is \(\boxed{1.8}\).
Examples
Proportions are used frequently in real life for scaling measurements. For instance, if you have a recipe that serves 3 people and requires 0.45 kilograms of flour, but you need to feed 12 people, you can use the proportion \(\frac{0.45}{3} = \frac{x}{12}\) to determine that you need \(1.8\) kilograms of flour. This ensures the ratios of ingredients remain consistent regardless of the number of servings.