Using distributive property to simplify multiplication:

Multiplication problems can often be simplified and solved using the distributive property. This property states that a multiplication problem can be broken down into smaller parts and then added together to find the final answer. Here are some examples of using the distributive property to simplify multiplication problems:

(a) 728 × 101:

To use the distributive property, we can break down 101 into its component parts, which are 100 and 1. We can then multiply each part separately and add the results together.

728 × 101 = 728 × (100 + 1)
= 72800 + 728
= 73528

Therefore, 728 × 101 = 73528.

(b) 5437 × 1001:

Again, we can break down 1001 into its component parts, which are 1000 and 1. We can then multiply each part separately and add the results together.

5437 × 1001 = 5437 × (1000 + 1)
= 5437000 + 5437
= 5442437

Therefore, 5437 × 1001 = 5442437.

(c) 4275 × 125:

We can break down 125 into its component parts, which are 100 and 25. We can then multiply each part separately and add the results together.

4275 × 125 = 4275 × (100 + 25)
= 427500 + 106875
= 149375

Therefore, 4275 × 125 = 149375.

(d) 824 × 25:

We can break down 25 into its component parts, which are 20 and 5. We can then multiply each part separately and add the results together.

824 × 25 = 824 × (20 + 5)
= 16480 + 4120
= 20600

Therefore, 824 × 25 = 20600.

(e) 504 × 35:

We can break down 35 into its component parts, which are 30 and 5. We can then multiply each part separately and add the results together.

504 × 35 = 504 × (30 + 5)
= 15120 + 2520
= 17640

Therefore, 504 × 35 = 17640.