When working with measurements you’ll occasionally need to add them together, and that can be intimidating when the measurements include feet, inches, and in fractions. Fortunately, adding feet and inch fractions can be done in a few simple steps.
Step One: Convert to a Common Unit of Measurement
The first step is to find some common ground among your measurements. Convert all feet measurements into inches, so they can be added together more easily. If a measurement is entirely in feet, or contains feet, start by converting feet into inches by multiplying feet by 12.
If the measurement contains feet and inches, split them apart into feet and inches first, so we can convert the feet to inches, then add them back together.
For example, convert the measurement 2 ft – 6 in to inches.
2′ 6″ = 2′ + 6″
2′ 6″ = (2 × 12) + 6″
2′ 6″ = 24″ + 6″
2′ 6″ = 30″
Step Two: Convert Inch Fractions to a Common Denominator
If you are working with fractions, the next step is to transform all the inch fractions in the equation into the same format so the denominators, or the bottom numbers, are all the same. This is a necessary step when adding or subtracting unlike fractions.
If all the fractions have the same denominator then move on to the next step.
To update fractions to all have the same denominator, start by finding the largest denominator of all the fractions. Then, for each remaining fraction divide the denominator by the larger denominator to find the multiplier. The final step will be to multiply both the numerator, or top number, and the denominator by this multiplier to create an equal fraction.
For example, convert the inch fractions 12, 14, and 18 to be like fractions with the same denominator.
First, find the largest denominator. The largest number among 2, 4 & 8 is 8.
Next, convert the inch fraction 12 to have a denominator of 8.
multiplier = big denominator ÷ small denominator
multiplier = 8 ÷ 2
multiplier = 4
fraction = 12
fraction = (1 × 4)(2 × 4)
fraction = 48
Finally, convert 14 to have a denominator of 8.
multiplier = 8 ÷ 4
multiplier = 2
fraction = 14
fraction = (1 × 2)(4 × 2)
fraction = 28
For more help on converting fractions, check out our unknown fraction calculator, which can help find the correct numerator for each fraction.
Step Three: Add or Subtract Inch Fraction Numerators
The next step is to add all the inch fractions together. This should be done before adding the whole inch measurements together. To add the fractions, add the numerators of the inch fraction measurements together. Finally, put the sum of the numerators over the original denominator.
For example, add the fractions from the previous example, which are 48, 28, and 18.
The numerators of these fractions are 4, 2 & 1. The denominator of all of them is 8.
numerator = 4 + 2 + 1
numerator = 7
So the resulting combined fraction is 78.
The process for subtracting is the same as adding, subtract the numerators from each other. If the fraction is negative it may need to be subtracted from the whole inches sum or difference in the next step.
Step Four: Add or Subtract Whole Inches
Now that the fractions have been consolidated into a single fraction it’s time to add the whole inches together. This step is pretty straight forward, add or subtract the whole inch measurements from each other.
For example, add the whole inches 24″ and 6″.
inches = 24″ + 6″
inches = 30″
Step Five: Convert the Inches to Feet and Inches
We’re nearly complete and it’s time to convert the sum or different in whole inches into feet and inches. To start, divide the whole inches from the previous step by 12. This might result in a decimal number, the number to the left of the decimal point is the feet measurement.
For example, find how many feet are in 30″.
decimal feet = 30″ ÷ 12
decimal feet = 2.5′
The number of whole feet is 2.
Now take the number of whole feet and multiply by 12.
inches = 2 × 12
inches = 24″
Then, subtract the number of whole feet in inches from the total number of inches to get the remainder.
remainder inches = 30″ – 24″
remainder inches = 6″
Finally, put the number of whole feet with the number of remainder inches, this is the feet and inches measurement.
whole feet = 2′
remainder inches = 6″
feet & inches = 2′ 6″
Our inches to feet & inches conversion calculator will help with this conversion.
Step Six: Reduce the Inch Fraction
You made it to the final step, great job! Now it’s time to reduce the remaining fraction to the smallest possible fraction. If the numerator of the inch fraction is odd, then it cannot be reduced, you’re done!
If the numerator is even, divide both the numerator and denominator by 2 to reduce by a power of 2. Continue doing this until the numerator is even.
For example, let’s reduce the inch fraction 28.
fraction = 28
fraction = (2 ÷ 2)(8 ÷ 2)
fraction = 14
Here’s a Tip: use our fraction simplifier to help simplify a fraction for a final result.
Inch and Foot Calculator
There has to be a better way! If you’re still stuck or would like some help adding or subtracting length measurement’s, use our inch fractions calculator to quickly and easily calculate inch, feet, and metric measurements.