How to Convert, Compare, Add, and Subtract Mixed Customary Units?

A step-by-step guide to converting, comparing, adding, and subtracting mixed customary units

The traditional system would be described as a set of weights and measures used for measuring length, weight, temperature, and capacity.

Lengths and distances will be measured in inches, feet, miles, and yards.

Use these rules to convert between traditional units:
Multiply to convert from a bigger unit to a lesser unit.
Divide to convert from a lesser unit to a bigger unit.

Here is a step-by-step guide on how to convert, compare, add, and subtract mixed customary units:

1. Understand the types of units involved: Mixed customary units are measurements that combine whole units and fractions. Identify the units involved in the problem and make sure you understand how to convert them.
2. Convert units to the same measurement: If you need to compare or perform operations on mixed customary units, you need to first convert them to the same unit of measurement. To do this, use conversion factors to convert each unit to the desired unit of measurement. For example, to convert feet to inches, multiply by \(12\) since there are \(12\) inches in a foot.
3. Compare the measurements: Once you have converted the mixed customary units to the same unit of measurement, compare them to determine which is larger or smaller. If the measurements have different units, convert them to the same unit first.
4. Add the measurements: To add mixed customary units, add the whole units and fractions separately. Make sure they are in the same unit of measurement before adding them together. If necessary, convert the sum back to mixed units.
5. Subtract the measurements: To subtract mixed customary units, subtract the whole units and fractions separately. Make sure they are in the same unit of measurement before subtracting. If necessary, convert the difference back to mixed units.
6. Check your work: Always check your work to make sure it makes sense in the context of the problem. Double-check your calculations and make sure you have the correct units.

Converting, Comparing, Adding, and Subtracting Mixed Customary Units – Example 1

Compare.
\(3kg \:Box 3500g\)
Solution:
\(1 kg=1000 g\)
Multiply \(3kg\) by \(1000\).
\(3×1000=3000 g\)
\(3000 g\) is less than \(3500g\). So, \(3kg<3500g\)

Converting, Comparing, Adding, and Subtracting Mixed Customary Units – Example 2

Add and subtract.
\(5 m 20 cm-2 m 70 cm=\:Box m\:Box cm\)
\(5 m 20 cm=520 cm\)
\(2 m 70 cm=270 cm\)
So, \(520-270= 250 cm\)
\(250 cm=2 m 50 cm\)