Question

Diego is trying to find the smallest product of a two-digit by three-digit number

using the numbers 1 through 5. He finds the product 14,040. Is there a smaller
product he could find using the numbers 1 through 5? Explain your reasoning.

Answer 1

Diego can find a smaller product than 14,040 for a two-digit by three-digit multiplication using the numbers 1 through 5. By choosing the smallest digits (12 and 135), he can get a product of 1,620, which is smaller than 14,040.

Step-by-step explanation:

The question asks if Diego can find a smaller product than 14,040 when multiplying a two-digit number by a three-digit number, using only the numbers 1 through 5. To create the smallest possible product, Diego should use the smallest digits in the largest places. For the two-digit number, the smallest possible combination is 12 (as we can't use 10, which doesn't encompass the digits 1 to 5). For the three-digit number, the smallest combination is 135. Now, when we calculate the product of 12 and 135, we get:

12 x 135 = 1,620

This product is indeed smaller than 14,040, suggesting that Diego can find a smaller product than the one he has by using the digits more strategically to minimize the product.