find the product using mental math and the distributive property for 7(15) showing the work as shown

70 + 35

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To find the product of 7 and 15 using mental math and the distributive property, you can break down the multiplication into simpler steps. Here's the step-by-step process:

Step 1: Start with the given equation: 7(15).
Step 2: Apply the distributive property, which states that a(b + c) = ab + ac. In this case, 7 is multiplied by the sum of 15.
Therefore, we can rewrite 7(15) as 7 × (10 + 5).
Step 3: Now, distribute 7 to both terms inside the parentheses by multiplying:
7 × 10 = 70
7 × 5 = 35
Step 4: Add the products obtained in step 3:
70 + 35 = 105.

So, using the distributive property, the product of 7 and 15 is 105.