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Newton wants to use regrouping to find 723 - 175. Is this a good strategy for him to use? Explain.

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Answer:

yes

Explanation:

You want to know if regrouping is a good strategy for computing 723 -175.

Regrouping

One "regroups" a number to make it easier (or possible) to carry out certain arithmetic operations. Here, there are several possible regrouping strategies that could be employed.

Strategy 1

The usual right-to-left digit-by-digit subtraction algorithm taught in US schools will require regrouping twice.

First regrouping, to compute the units digit of the result:

723 -175 = 710 +13 -170 -5 = (710 -170) +(13 -5) = (710 -170) +8

Second regrouping to compute the tens digit of the result:

= (600 -100) +(110 -70) +8 = (600 -100) +40 +8 = (600 -100) +48

The hundreds digit of the result can be computed without any further regrouping:

= 500 +48 = 548

Strategy 2

The left-to-right subtraction taught in other places also requires regrouping for computing the tens and units digits:

723 -175 = (723 -100) -75 = 623 -75 . . . . no regrouping yet

= 623 +(-100+30) -5 = 553 -5 . . . . regrouping for tens digit

= 553 +(-10 +5) = 548 . . . . . regrouping for units digit

Strategy 3

The subtrahend can be rewritten so that no carries or borrows are required. This is perhaps the easiest of the regrouping strategies to use:

723 -175 = 723 +(-200 +25) = 523 +25 = 548

Regrouping is a good strategy to use for this subtraction problem.

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