#### What is the distributive property of 7×6?

**Final Answer:**

The distributive property allows us to simplify multiplication over addition, shown as a×(b+c)=a×b+a×c. By applying this with 7×6 as 7×(3+3) or 7×(5+1), we confirm that the answer is 42. Thus, the property helps us find the same result using different breakdowns of the numbers.

**Explanation:**

The distributive property is a helpful mathematical rule that allows us to break down multiplication across addition. It states that for any numbers a, b, and c, the rule is as follows:

a×(b+c)=a×b+a×c

To see how this works with the specific example of 7×6, we can use the distributive property by breaking down the number 6. Let’s rewrite 6 as 3 + 3:

7×6=7×(3+3)

Now we apply the distributive property:

7×(3+3)=7×3+7×3

Calculating each part gives:

7×3=21

So then:

7×3+7×3=21+21=42

This shows that:

7×6=42

We could also break down 6 differently, for example, as 5 + 1:

7×6=7×(5+1)

Then applying the distributive property again:

7×(5+1)=7×5+7×1

Calculating each part gives:

7×5=35

And:

7×1=7

So:

35+7=42

This also verifies that 7×6=42. Thus, the distributive property is a powerful tool for simplifying multiplication problems.

Examples & Evidence

For instance, to calculate 8×5, we could rewrite 5 as 2 + 3 and apply the distributive property: 8×5=8×(2+3)=8×2+8×3=16+24=40.

The distributive property is a fundamental principle in mathematics and can be found in any algebra textbook or educational resource that covers basic arithmetic and algebra concepts.

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