Express the following ratios in the simplest form 4 litres to 250 ml
The Correct Answer and Explanation is:
Simplified Ratio:
4 litres to 250 millilitres = 16:1
Step-by-step Conversion and Simplification
To simplify a ratio, the units must be the same. Here, one value is in litres and the other in millilitres, so we first convert them to the same unit.
1 litre = 1000 millilitres
So,
4 litres = 4 × 1000 = 4000 millilitres
Now the ratio is:
4000 ml : 250 ml
Now, divide both terms by their greatest common divisor (GCD).
GCD of 4000 and 250 is 250.
Now divide:
- 4000 ÷ 250 = 16
- 250 ÷ 250 = 1
So, the simplified ratio is 16:1
Explanation
Ratios express how much of one quantity there is compared to another. They are used in many real-life situations like recipes, maps, and business to show relationships between amounts. To accurately interpret and compare ratios, it’s essential that the units in both quantities are consistent. If the units differ—as in the case of litres and millilitres—conversion is required before simplification.
In this question, we are given a ratio of 4 litres to 250 millilitres. Since litres and millilitres are both units of volume, but on different scales, we need to convert them to the same unit to simplify. It’s generally easier to convert litres to millilitres because it avoids decimals. Since 1 litre equals 1000 millilitres, 4 litres equals 4000 millilitres.
So, the ratio becomes 4000 millilitres to 250 millilitres. At this point, the ratio is just two numbers with the same units, and we can proceed to simplify by dividing both by the greatest common divisor (GCD). In this case, the GCD of 4000 and 250 is 250. Dividing both numbers by 250 gives the simplified form 16:1.
This means that for every 16 parts of the first quantity (litres), there is 1 part of the second quantity (millilitres). The simplification removes the units, providing a clear, proportional comparison. It helps in understanding and applying the ratio in practical contexts, such as mixing solutions or converting measurements in recipes or industrial processes.
