How to add mixed measures
Some conversion formulas for adding mixed measures
Mixed measures are measurements like hours, minutes and seconds, or yards, feet, and inches.
It’s fairly simple to understand the distance
???3\text{ yards},\ 2\text{ feet},\ 4\text{ inches}???
If we want to add two sets of mixed measures, the method we use is essentially the same thing we do when we add mixed numbers. First, we add the individual measures, like hours or minutes, or yards or feet, separately. That’s the easy part. The trickier part is the second part, which is simplifying the result of the first part.
As a reminder, here are some conversion formulas to use in these kinds of problems:
???1??? yard = ???3??? feet = ???36??? inches
???1??? hour = ???60??? minutes = ???3,600??? seconds
How to add mixed measures by rolling smaller measures into larger measures
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Adding yards, feet, and inches
Example
Find the sum of the mixed measures.
???3\text{ yards},\ 2\text{ feet},\ 4\text{ inches}???
???6\text{ yards},\ 2\text{ feet},\ 8\text{ inches}???
First, we’ll add the yards, the feet, and the inches separately.
???(3+6)\text{ yards},\ (2+2)\text{ feet},\ (4+8)\text{ inches}???
???9\text{ yards},\ 4\text{ feet},\ 12\text{ inches}???
We’ve now converted the sum of the two original sets of mixed measures to a single set of mixed measures. Since ???12??? inches is equivalent to ???1??? foot, we want to simplify that result so that the number of inches is less than ???12???. We do this by working from right to left. We’ll first rewrite ???12??? inches as ???1??? foot, and then we’ll add that ???1??? foot to the ???4??? feet we’ve already found:
???9\text{ yards},\ 4\text{ feet},\ 12\text{ inches}???
???9\text{ yards},\ 4\text{ feet},\ 1\text{ foot}???
???9\text{ yards},\ (4+1)\text{ feet}???
???9\text{ yards},\ 5\text{ feet}???
Since there are ???3??? feet in a yard, we want to simplify that result so that the number of feet is less than ???3???. We’ll first express ???5??? feet as the sum of ???3??? feet and ???2??? feet, then rewrite ???3??? feet as ???1??? yard, and add that ???1??? yard to the ???9??? yards we’ve already found:
???9\text{ yards},\ 3\text{ feet}+2\text{ feet}???
???9\text{ yards},\ 1\text{ yard}+2\text{ feet}???
???(9+1)\text{ yards},\ 2\text{ feet}???
???10\text{ yards},\ 2\text{ feet}???
This is the sum of ???3\text{ yards},\ 2\text{ feet},\ 4\text{ inches}??? and ???6\text{ yards},\ 2\text{ feet},\ 8\text{ inches}???.