Long multiplication and division: two-digit numbers

A zero inside the number does not change the place values of other digits. Keep digits aligned by place value, calculate both partial products and add them.

The remainder must be smaller than the divisor. Find how many more times the divisor fits into the reported remainder. Add that number to the reported quotient and subtract the corresponding divisor product from the reported remainder. Check both requirements: divisor × quotient + remainder = dividend and 0 ≤ remainder < divisor.

Multiply the divisor by the displayed quotient and subtract this product from the dividend. The remainder must be non-negative and smaller than the divisor.

The second partial product represents multiplication by tens: multiply the first number by the tens digit and by 10. Do not treat tens as units.

Starting from the left, take the shortest dividend prefix at least as large as the divisor. Find a quotient digit, multiply, subtract and bring down the next digit. Repeat. Check: divisor × quotient = dividend.

Multiply by the units digit and by the tens digit. Multiply the tens partial product by 10, then add the two partial products.

Add the displayed partial products with digits aligned by place value. Answer with the hidden digit only, not the whole product.

When bringing down a digit gives a number smaller than the divisor, write 0 in the quotient. Then bring down another digit. Do not omit the zero, because it preserves the quotient place values.