Why do you multiply to change from larger unit to a smaller unit?

because there are more smaller units in a given quantity

There are more dimes than quarters in a dollar, right?

Well, multiplying to change from a larger unit to a smaller unit is like using a "miniaturization ray" on your measurement. You're basically squeezing more of those smaller units into the larger unit. It's like trying to fit more clowns into a tiny car – the more you multiply, the more tiny clowns you can fit! So, multiplying helps you convert between units and have some fun with clowns at the same time. Win-win!

Multiplication is used to change from a larger unit to a smaller unit because the relationship between different units of measurement is based on equal proportions.

When you multiply a larger unit by a conversion factor, which is a ratio of the smaller unit to the larger unit, you are essentially multiplying by 1. This preserves the value while changing the units.

For example, when converting from meters to centimeters, there are 100 centimeters in 1 meter. So, to convert 2 meters to centimeters, you would multiply 2 meters by the conversion factor of 100 centimeters/meter:

2 meters * (100 centimeters/meter) = 200 centimeters

By multiplying by the conversion factor, you are effectively canceling out the meters and ending up with centimeters.

In general, multiplying by the conversion factor allows you to scale the value from one unit to another while maintaining the same quantity.

When you multiply to change from a larger unit to a smaller unit, you are essentially converting from a higher order of magnitude to a lower order of magnitude. This happens because each smaller unit is a fraction of the larger unit.

To understand why multiplication is used for this conversion, let's take a simple example of converting from meters (m) to centimeters (cm).

1 meter is equivalent to 100 centimeters. Now, if we want to convert 3 meters to centimeters, we need to multiply it by the conversion factor, which is 100.

So, 3 meters x 100 = 300 centimeters.

Here's why multiplication works:
- Multiplying 3 meters by 100 gives us 300, which means we have 300 of the smaller unit (centimeters).
- Since 1 meter is equivalent to 100 centimeters, multiplying by 100 allows us to account for the conversion from a larger unit (meters) to a smaller unit (centimeters).

In general, when converting from a larger unit to a smaller unit, you need to multiply by the appropriate conversion factor, which represents the ratio between the two units (e.g., 100 for meters to centimeters, 60 for minutes to seconds).

The reason it's multiplication and not division is because each smaller unit is a fraction of the larger unit. By multiplying, you are essentially scaling up the value by the appropriate conversion factor.