Definition
Partial differences
Partial differences subtract matching place-value parts separately, then combine those differences.
Continue from this idea into connected AXIO math.
Defining relationship
Find a difference in each place, then put the place-value differences together.
Partial differences is a place-value subtraction method. The minuend and subtrahend are decomposed by place, corresponding parts are subtracted to produce partial differences, and those signed differences are combined to obtain the total difference.
A negative partial difference is valid; combine the place differences at the end.
What it means
Break both numbers into hundreds, tens, and ones. Find the difference in each place, keep a minus sign when one part is below zero, and then combine the pieces. For 86 − 24, the tens give 80 − 20 = 60 and the ones give 6 − 4 = 2, so 60 + 2 = 62.
Remember it
Find a difference in each place, then put the place-value differences together.
Example
Find 352 − 127. Hundreds: 300 − 100 = 200. Tens: 50 − 20 = 30. Ones: 2 − 7 = −5. Combine the partial differences: 200 + 30 − 5 = 225. The negative ones difference means the ones part is short by 5.
Watch for
Subtracting 127 as 100, then 20, then 7 from a running total is a different left-to-right decomposition strategy, not the place-by-place partial-differences method owned here.
Common mix-up
A negative partial difference is not automatically an error; its sign must be kept when all partial differences are combined.
Exact meaning
Partial differences is a place-value subtraction method. The minuend and subtrahend are decomposed by place, corresponding parts are subtracted to produce partial differences, and those signed differences are combined to obtain the total difference.