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How to Regroup in Math While Carrying in Multiplication

Regrouping implements the distributive property of multiplying each addend in a multi-digit number by the same number and adding the individual products to find a sum. For example, 62 x 3 = 3(60 + 2). In this case, the 3 is distributed to 60 and 2, as in 3 x 60 = 180 and 3 x 2 = 6. Add the products of 180 and 6 for a sum of 186. You can implement a multiplication shortcut of the distributive property by regrouping through carrying a digit and placing it above the digit to the left of the one being multiplied, simplifying the addition step of the distributive property.

Instructions

    • 1

      Write your multiplication problem down vertically, lining up corresponding digits. Place the number with the least amount of digits on the bottom row, as in:

      34

      x 5

    • 2

      Multiply the digit in the ones place on the top row by the digit in the ones place on the bottom row. For example, in 34 x 5, multiply the 4 in the ones place by the 5 in the ones place to find a product of 20.

    • 3

      Place the digit in the ones place of the product under the answer line in the ones place. In the case of the example 34 x 5, place the 0 from the product 20 under the answer line.

    • 4

      Carry the digit in the tens place of your product by placing it above the number located in the tens place to regroup. For example, carry the number 2 from the product 20 and place it above the 3 in the tens place of the problem. The regrouping process is the concept of separating and simplifying groups of 10 ones. For instance, 20 equals 10 ones +10 ones + 0 ones. This means the 20 ones can be regrouped and carried as 2 sets of 10 ones.

    • 5

      Multiply the digit in the tens place of the top row by the digit in the ones place of the bottom row. For instance, in the problem 34 x 5, multiply the 3 by the 5 to find a product of 15.

    • 6

      Add the product of multiplying the tens place with the number that you carried. In the example of 34 x 5, the product of the tens place is 15 and the carried number is 2 for a sum of 17.

    • 7

      Place the total underneath the number line for a total of 170, in the case of the example, if multiplying a two-digit number. Continue the pattern of placing the ones digit in the product under the number line and carrying the tens digit, if the number on the top row has more than two digits by which to multiply.

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