Find the ratio of ( 250 , ml ) to ( 1.5 , l ) in its simplest form.
a) ( 1:6 )
b) ( 1:15 )
c) ( 1:600 )
d) ( 1:1500 )
The Correct Answer and Explanation is :
To find the ratio of 250 ml to 1.5 liters in its simplest form, let’s follow these steps:
- Convert units: We need both quantities in the same unit for a straightforward comparison. Since 1 liter (L) equals 1,000 milliliters (ml), convert 1.5 liters to milliliters:
[
1.5 \text{ L} = 1.5 \times 1000 \text{ ml} = 1500 \text{ ml}
] - Set up the ratio: Now, we have 250 ml and 1500 ml. The ratio is therefore:
[
250 : 1500
] - Simplify the ratio: To express the ratio in its simplest form, divide both terms by their greatest common divisor (GCD). Here, the GCD of 250 and 1500 is 250:
[
\frac{250}{250} : \frac{1500}{250} = 1 : 6
] - Conclusion: The simplest form of the ratio is 1:6.
So, the correct answer is:
a) ( 1:6 )
Explanation
Ratios are often used to compare two quantities of the same unit by showing how many times one quantity contains another. To simplify ratios, both quantities must first be in the same unit, as it allows for easy comparison and simplification. Here, by converting 1.5 liters to milliliters, we avoided a mixed-unit calculation.
After converting, we had 250 ml to 1500 ml, which simplified to 1:6. Simplifying a ratio involves dividing both terms by the GCD to get the smallest integer values, preserving the proportion without changing its meaning. Therefore, this solution shows that 250 ml is six times less than 1.5 liters, hence the answer (1:6).