Simplify $3 L: \frac{1}{2} L: \frac{3}{4} L: 1 L$
Answer (2)
The simplified form of the ratio 3 L : 2 1 L : 4 3 L : 1 L is 12 : 2 : 3 : 4 . This was achieved by dividing through by L and then multiplying by the least common multiple of the denominators to clear the fractions. The final simplified ratio is 12 : 2 : 3 : 4 .
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Divide each term in the ratio by L : 3 : 2 1 : 4 3 : 1 .
Multiply each term by 4 to eliminate fractions: 3 ( 4 ) : 2 1 ( 4 ) : 4 3 ( 4 ) : 1 ( 4 ) .
Simplify the resulting ratio: 12 : 2 : 3 : 4 .
The simplified ratio is 12 : 2 : 3 : 4 .
Explanation
Understanding the Ratio We are given the ratio 3 L : 2 1 L : 4 3 L : 1 L . Our goal is to simplify this ratio.
Removing the Units First, we divide each term by L to get rid of the units. This gives us the ratio 3 : 2 1 : 4 3 : 1 .
Eliminating Fractions Next, we want to eliminate the fractions. To do this, we multiply each term in the ratio by the least common multiple of the denominators, which is 4. This gives us:
3 × 4 : 2 1 × 4 : 4 3 × 4 : 1 × 4
Performing the Multiplications Now, we perform the multiplications:
12 : 2 : 3 : 4
Final Simplified Ratio Thus, the simplified ratio is 12 : 2 : 3 : 4 .
Examples
Ratios are used in everyday life, such as when baking a cake. If a recipe calls for a ratio of flour to sugar to butter of 3:2:1, and you want to make a larger cake, you can use this ratio to scale up the ingredients proportionally. Similarly, in mixing paints, a ratio can define the proportions of different colors needed to achieve a desired shade. Understanding ratios helps ensure that the final product maintains the intended balance and consistency.
