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Everyday MathematicsPartial-Differences Subtraction

Partial-Differences SubtractionPartial-differences subtraction involves:Thinking about numbers in expanded notation;Using place value to determine partial differences; andAdding partial differences.

Everyday Mathematics

Partial-Differences SubtractionSolve: 471 293We begin by thinking about each number in expanded notation.471 = 400 + 70 + 1293 = 200 + 90 + 3We can subtract in any place-value order. Everyday Mathematics 471 293

Partial-Differences SubtractionSolve: 471 293Everyday Mathematics 471 293

Lets start with the hundreds place.471 = 400 + 70 + 1293 = 200 + 90 + 3

400 200 = 200

Partial-Differences SubtractionSolve: 471 293

Everyday Mathematics 471 293Now we subtract the tens.Since we are subtracting a larger400 200 = 200number from a smaller number, the difference is negative.

471 = 400 + 70 + 1293 = 200 + 90 + 3

70 90 = 20

Partial-Differences SubtractionSolve: 471 293

471 293

400 200 = 20070 90 = 20

Everyday MathematicsFinally, we subtract the ones. 471 = 400 + 70 + 1293 = 200 + 90 + 3Since we are subtracting a largernumber from a smaller number, the difference is negative. 1 3 = 2

Partial-Differences SubtractionSolve: 471 293Everyday Mathematics 471 293We add the partial-differences to find the total. 20020+ 2178

471 293 = 178

Partial-Differences SubtractionWhen children use partial-differences subtraction they practice

Everyday Mathematicsa variety of skills related to number sense and algebraic reasoning. For example:Thinking about numbers in expanded notation;Using place value to determine partial differences; andAdding positive and negative numbers.If children start with the largest place value, which is generally

their inclination, they begin the problem-solving process with a

reasonable estimate of what the final answer should be.