Multiplication with Distributive Property

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What is the Distributive Property?

The distributive property is a handy way of breaking down more complex multiplication problems into simpler ones. It’s like taking a big problem and splitting it into smaller, more manageable pieces. The property says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately and then adding the results.

Basic Formula

The basic formula of the distributive property looks like this:
a×(b+c)=a×b+a×c

Real-life Examples

  1. Buying Fruits: Imagine you’re at a store buying 3 apples and 3 bananas. Each apple costs $2 and each banana costs $3. Instead of calculating the total price separately, you can use the distributive property. Here’s how:3×(2+3)=3×2+3×3

    This means buying 3 apples and 3 bananas is the same as buying 3 fruits priced at $2 each plus 3 fruits priced at $3 each.

  2. Sharing Cookies: Suppose you have 4 packets of cookies. Each packet contains 5 chocolate and 3 strawberry cookies. To find out how many cookies you have in total, you can use the distributive property:4×(5+3)=4×5+4×3

    This means you have the same number of cookies as if you had 4 packets of 5 chocolate cookies plus 4 packets of 3 strawberry cookies.

Explanation of Answers

Using the fruit example:

3×(2+3)=3×2+3×3 3×5=6+9 15=15

So, whether you add the prices of the apple and banana first (which makes $5), and then multiply by 3, or you multiply each fruit’s price by 3 and then add them, you’ll end up spending the same amount, $15.

Tips

  • Break It Down: When faced with a big multiplication problem, break it down into smaller parts.
  • Practice with Objects: Use objects around you, like fruits or toys, to understand the concept better.
  • Check Your Work: After using the distributive property, you can always multiply the original way to make sure your answer is correct.

Remember, the distributive property is just a tool to make multiplication easier and more fun! Keep practicing, and you’ll get the hang of it in no time!

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