Customary Unit Conversions Involving Mixed Numbers and Fractions

A step-by-step guide to Customary Unit Conversions Involving Mixed Numbers and Fractions

Converting customary units involving mixed numbers and fractions can be a bit tricky, but it is a useful skill to have in many real-world situations. Here is a step-by-step guide to help you through the process:

1. Identify the starting unit and the desired unit. For example, you might be given a measurement in feet and need to convert it to inches.
2. Determine the conversion factor between the two units. This is a ratio that relates the starting unit to the desired unit. For example, to convert from feet to inches, you would use the conversion factor 12 inches/1 foot.
3. Write the mixed number or fraction as an improper fraction. To do this, multiply the whole number by the denominator and add the numerator. For example, 2 1/2 would become 5/2.
4. Multiply the numerator of the mixed number or fraction by the conversion factor. This will give you the number of desired units for that part of the mixed number or fraction. For example, if you were converting 2 1/2 feet to inches, you would multiply 1/2 (the fractional part) by 12 (the conversion factor), giving you 6 inches.
5. Add the result from step 4 to the product of the whole number and the conversion factor. This will give you the total number of desired units. For example, if you were converting 2 1/2 feet to inches, you would add 24 (2 times 12) and 6, giving you 30 inches.
6. Write the final answer as a mixed number or fraction, if desired. To do this, divide the total number of desired units by the conversion factor and write the result as a mixed number or fraction, with any remainder as the numerator and the conversion factor as the denominator. For example, if you had 30 inches and wanted to write the answer as a mixed number, you would divide by 12 (the conversion factor) to get 2 with a remainder of 6. The answer would be 2 1/2 feet.
7. Check your work. Make sure your final answer makes sense and that you have used the correct units.

With practice, you will become more comfortable with converting mixed numbers and fractions in the customary system. Remember to take your time and double-check your work to ensure accuracy.

Customary Unit Conversions Involving Mixed Numbers and Fractions – Example 1

Convert. Simplify and write as a fraction or whole or mixed number.
\(5yd=\)_____in
Solution:
Multiply a larger unit by a smaller unit to convert.
\(1yd=36\) in
\(5×36=180\) in

Customary Unit Conversions Involving Mixed Numbers and Fractions – Example 2

Convert. Simplify and write as a fraction or whole or mixed number.
____\(ft=\frac{4}{5}\) mi
\(1 mi=5280\) ft
Divide to convert from a lesser unit to a bigger unit.
\(5280÷5=1056\)
\(1056×4=4224\)
So, \(4224 ft=\frac{4}{5}\) mi