Checking the Four Processes

Although most students use calculators now, here is what can be done to check questions using the four basic processes when one is not available. A calculator is faster and more accurate, but all students should be able to perform the four processes in one's head or with pencil and paper.

Addition

Method 1 -- If you add the columns up, check by adding down. The two answers should be the same.
Method 2 -- Add the digits in the first horizontal row (addend). Divide the total by 9. Write down the remainder. Do the same with each horizontal row above the line (other addends). Add the remainders and divide by 9. Write down the remainder. Now, add the digits of the sum of the original column. Divide by 9. Write down the remainder. The two final remainders should be the same.

Subtraction

Method 1 -- Add your difference and the number just above the line (subtrahend). Your answer should be the top number from which you subtracted (minuend).
Method 2 -- Add the digits in the first horizontal row. Divide the total by 9. Write down the remainder. Do the same with the digits in the second row. Subtract the two remainders. Add the digits of the difference row. Divide by 9. Write down the remainder. The two remainders should be the same.

Multiplication

Method 1 -- Divide the answer (product) by the number just above the line (muliplier). The result should be the top number (multiplicand).
Method 2 -- Add the digits of the multiplicand. Divide by 9. Write the remainder. Do the same with the multiplier. Multiply the two remainders. Divide by 9. Write the remainder. Add the digits of the product. Divide by 9. Write the remainder. The two final remainders should be the same.

Division

Method 1 -- Multiply the answer on top (quotient) by the number by which you had divided (divisor). Add the remainder. The result should be the number that you were dividing (dividend).
Method 2 -- Add the digits of the quotient. Divide by 9. Write the remainder. Do the same with the digits of the divisor and the remainder in the question. Multiply the remainders of the quotient and the divisor. Add the remainder from the remainder of the question. Divide by 9. Write the remainder. Add the digits of the dividend. Divide by 9. Write the remainder. The two final remainders should be the same.