I'm working on conversions and can't ever figure out when I need to multiply and when I need to divide.
For example - 50L = ? gal
I know 3.79 L = 1 gal but do I divide or multiple to get the correct answer?
Or, 2 mi = ? m
I know 1 m = 3.28 ft and 5280 ft = 1 mile, but I don't know in what order to use those, or how to figure out HOW to use them.
Is there an easy rule of them to know if you use multiplication or division?
Thank you.
watch the units. They cancel out just like numbers.
3.79L = 1gal, so
3.79L/1gal = 1
1gal/3.79L = 1
you can always multiply by 1 without changing anything, so use the fraction which cancel the undesired units.
50L * 1gal/3.79L = 50/3.79 gal
see? The L units canceled out, leaving just gals.
easy rule: keep your units in the equation:
50L*( ) so you want L to divide out, so you multiply
50L*(1gal/3.79L)= 50/3.79 gallons
2 mile( ) you need miles to divide out, so you 2miles(5280ft/mile) and that give you feet. But you want more, you want meters
2*5280ft( ) ft has to divide out, so
2*5280ft(1m/3.28ft) and then you have it.
When dealing with unit conversions, knowing whether to multiply or divide comes down to understanding the relationship between the units. Here are some guidelines to help you determine whether to multiply or divide:
1. Identify the relationship between the units: Look for the conversion factor that relates the two units in question. In your first example, you have the conversion factor 3.79 L = 1 gal, and in the second example, you have 1 m = 3.28 ft and 5280 ft = 1 mile.
2. Decide which unit you want to convert: Determine which unit you are starting with and which unit you want to convert to. In your first example, you want to convert 50 L to gallons, and in your second example, you want to convert 2 miles to meters.
3. Determine the desired unit placement: Position the conversion factor in a way that allows the units to cancel out correctly.
- If you want to convert from a larger unit to a smaller unit (e.g., gallons to liters or miles to feet), use multiplication. Multiply by the conversion factor where the larger unit is in the numerator and the smaller unit is in the denominator. This ensures that the units cancel out properly, leaving you with the desired unit.
- Conversely, if you want to convert from a smaller unit to a larger unit (e.g., liters to gallons or feet to miles), use division. Divide by the conversion factor where the smaller unit is in the numerator and the larger unit is in the denominator. Again, this ensures proper unit cancellation.
Now let's apply these guidelines to your examples:
Example 1: 50 L = ? gal
Since you want to convert from liters (L) to gallons (gal), which are larger units, you need to use multiplication. The conversion factor is 3.79 L = 1 gal. So, to convert, multiply 50 L by the conversion factor:
50 L * (1 gal / 3.79 L) = 13.19 gal (rounded to two decimal places)
Example 2: 2 mi = ? m
In this case, you want to convert from miles (mi) to meters (m), which are smaller units. Therefore, you should use multiplication. Start by converting miles to feet using the conversion factor 5280 ft = 1 mile:
2 mi * (5280 ft / 1 mi) = 10560 ft
Next, convert feet to meters using the conversion factor 1 m = 3.28 ft:
10560 ft * (1 m / 3.28 ft) = 3218.9 m (rounded to one decimal place)
By following these guidelines, you can ensure that you use the correct operation (multiplication or division) when converting units.