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Fractions: Changing a Subtraction Problem with Borrowing into a Basic Addition Problem
I encourage my students to share the tricks they’ve figured out with me. A couple years back, I had a student who told me that when they are subtracting and have to borrow, they subtract the number from the 10 and then add the result. For example: 23–8, they borrow 10 from the 20, and subtract 8 from it, leaving 2, and then add the 2 and the 3 to get 5, making the answer 15.
We can use that same technique when subtracting fractions. Let’s subtract 2 1/2–2/3.
We take a whole from the 2, and instead of adding it to the 1/2, we cut it in thirds and subtract the 2/3 from that. Then we have 1/2 + 1/3 left over.
This is easier than adding it to the 1/2 to make 3/6 and then finding the common denominator and subtracting because the numbers are smaller and adding is intrinsically easier than subtracting. We do the subtracting using easy numbers.
