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Step-by-Step Long Division With Remainders

Long division strikes fear into the heart of many a grade-school student. However, it need not be terrifying. Long division is the process of dividing one number (the dividend) by another (the divisor) to get an answer (the quotient). Sometimes the divisor does not go into the dividend equally, in which case the answer will include a remainder. The remainder, which is designated by the letter "r," must be less than the divisor.

Instructions

    • 1

      Place the dividend inside the division frame and the divisor outside on the left. In the problem 435 ÷ 25, 435 is the dividend and 25 is the divisor.

    • 2

      Divide the first digit in the dividend by the divisor. Since 25 does not go into 4, the next step is to divide the first and second digits in the dividend by the divisor. Since 25 goes into 43 once, write a 1 above the 3.

    • 3

      Multiply the number on top of the division frame by the divisor. Since 1 x 25 equals 25, write that number below the 43 and draw a line under it.

    • 4

      Subtract 25 from 43. The answer is 18. Now bring down the next number of the dividend, which is 5. Adding the 5 onto the end of 18 makes the new number 185.

    • 5

      Divide 185 by the divisor, 25. Because 25 can go into 185 seven full times, write 7 above the 5 (next to the 1 on top of the division frame).

    • 6

      Multiply 7 by the divisor, 25, which gives an answer of 175. Write 175 under the 185 at the bottom of the equation and draw a line under it. Subtract 175 from 185 to find the remainder, which is 10.

    • 7

      Write the remainder at the top of the equation with the rest of the answer. The complete answer for the problem 435 ÷ 25 is 17 with a remainder of 10.

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