show 2 ways of using the distributive property to find the product of 125 times 32
To use the distributive property to find the product of 125 times 32, we can break down these numbers into smaller components and then apply the distributive property in two different ways. Let's explore these methods:
Method 1: Breaking down 125 and 32 into smaller components
1. Decompose 125 into 100, 20, and 5: 125 = 100 + 20 + 5
2. Now apply the distributive property to each component:
125 * 32 = (100 + 20 + 5) * 32
= 100 * 32 + 20 * 32 + 5 * 32
= 3200 + 640 + 160
= 4000
Method 2: Breaking down 32 into smaller components
1. Decompose 32 into 30 and 2: 32 = 30 + 2
2. Apply the distributive property by multiplying each component separately and adding the results:
125 * 32 = 125 * (30 + 2)
= 125 * 30 + 125 * 2
= 3750 + 250
= 4000
Both methods yield the same result, which is 4000. Using the distributive property allows us to break down the multiplication into simpler calculations, making it easier to compute the final product.