Find Missing Digits a b and c in Multiplication Problem

Published on August 24, 2026

Pre-Algebra

Learn how to solve for the unknown digits a, b, and c in a decimal or multi-digit multiplication problem by analyzing partial products step by step.

Question

Answer

To find the values for

, and

, we need to analyze the given long multiplication problem step by step.

The problem is:

Step 1: Analyze the first partial product

The first partial product is the result of multiplying

.
The last digit of the product is

. The

is written down, and

is carried over to the next column.
The next column is

. The result ends in

The only single digit

that satisfies

ending in

Let’s verify this with the whole first partial product:
If

, then

.
Comparing

with the given

, we see that

Step 2: Analyze the second partial product

The second partial product is the result of multiplying

(or

with a

at the end).
We know

, so the number is

.
Adding the trailing zero for the tens place, we get

.
Comparing

with the given

, we see that

Step 3: Verify the final sum

Now we check if the sum of the partial products equals the final result:

This matches the final result given in the problem.

Final Values:

Theorems

• Standard Multiplication Algorithm

The standard algorithm for multiplying multi-digit numbers involves multiplying the multiplicand by each digit of the multiplier from right to left (representing ones, tens, hundreds, etc.), generating partial products, and then summing these partial products to obtain the final product.

• Distributive Property of Multiplication over Addition

The distributive property states that multiplying a number by a sum is the same as doing each multiplication separately: