Simplify $3 L: \frac{1}{2} L: \frac{3}{4} L: 1 L$
Answer (2)
To simplify the given ratio 3 L : 2 1 L : 4 3 L : 1 L , we first divide by L , leading to 3 : 2 1 : 4 3 : 1 . We then eliminate the fractions by multiplying each term by 4, resulting in the final simplified ratio of 12 : 2 : 3 : 4 .
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Divide each term in the ratio by L to get 3 : 2 1 : 4 3 : 1 .
Multiply each term in the ratio by 4 to eliminate the fractions: ( 3 × 4 ) : ( 2 1 × 4 ) : ( 4 3 × 4 ) : ( 1 × 4 ) .
Simplify the ratio to 12 : 2 : 3 : 4 .
The simplified ratio is 12 : 2 : 3 : 4 .
Explanation
Understanding the Problem We are given the ratio 3 L : 2 1 L : 4 3 L : 1 L . Our goal is to simplify this ratio.
Dividing by L First, we divide each term in the ratio by L . This gives us the ratio 3 : 2 1 : 4 3 : 1 .
Multiplying by 4 Next, we want to eliminate the fractions in the ratio. 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 ) 12 : 2 : 3 : 4
Final Answer Therefore, the simplified ratio is 12 : 2 : 3 : 4 .
Examples
Ratios are used in everyday life, such as when cooking, mixing paints, or calculating distances on a map. For example, if a recipe calls for a ratio of 1 part flour to 2 parts water, understanding ratios helps you scale the recipe up or down while maintaining the correct proportions. Similarly, when mixing paint colors, ratios help you achieve the desired shade by combining different colors in specific proportions. In map reading, ratios are used to represent the relationship between distances on the map and corresponding distances in the real world, allowing you to estimate actual distances between locations.
