Division of multi-digit whole numbers by two-digit whole-number divisors is understood as decomposing a dividend into place-value groups, determining the quotient through estimation and successive multiplication, and representing any remainder as a quantity smaller than the divisor. The standard algorithm or partial-quotients representations are connected to the inverse relationship between multiplication and division, with solutions checked by multiplying the divisor by the quotient and adding the remainder; decimal quotients and division involving fractions are outside this scope.
To divide by a two-digit number, use multiplication to estimate each quotient digit. After each subtraction, bring down the next digit. The remainder must always be less than the divisor.
Example:
Look at the first two digits, . Since fits into one time, write in the tens place of the quotient.
Subtract:
Bring down the next digit, . Now you have .
Since , write in the quotient.
Bring down the last digit, . Now you have .
Since , write in the quotient.
So,
The remainder is less than the divisor , so the answer is complete.
Check using multiplication:
Because the check gives the original dividend, the answer is correct.
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