Distributive Property of Multiplication

Big 'Arry seems upset, it looks like Sheriff Squeaks is needed! "Big 'Arry! What seems to be the problem?" "Help! I don't know how many squares I have in all, but apparently, the Lil 'Arry's can help!" Let's help Sheriff Squeaks calculate how much Big 'Arry has in all by using the distributive property of multiplication. Distribute simply means to give out, so the distributive property of multiplication teaches us that breaking down one factor, or number, into smaller parts to multiply them separately by the other factor, and adding the products together gives the same product as multiplying the two factors together. The distributive property of multiplication is very useful, because you can break down bigger multiplication problems into smaller ones! Let's practice with four times six. We can set up an array to model this problem. Break down one of the factors into smaller numbers that add up to the factor. For this problem, we will break down the six into three plus three. Next, distribute, or give out, the factor outside the parenthesis to each number inside the parentheses which is four times three for both. We can make two arrays with four rows of three to help. Now, find the products of the two smaller factor pairs. Four times three gives a product of twelve. We can check the answer by counting the arrays. Finally, add together the products. This means we will find the sum of twelve plus twelve... which is twenty-four. Let's check the answer by finding the product of the original problem! The product of the original problem is twenty-four, so the answer is correct! Now we have looked at the distributive property of multiplication and how it works, let's help Sheriff Squeaks calculate how many squares Big 'Arry has in all! Big 'Arry is seven rows by five, so set up an array with seven rows of five! What is the next step? Break down one of the factors! Since multiples of fives are easier than multiples of seven, let's break down the seven. How can we break down the seven? We can break the seven into four plus three. What is the next step? Distribute the outside factor, five, to the two numbers inside the parentheses. What should we do next? Find the product of both! Four times five equals twenty, and three times five equals fifteen! Check your work by counting the arrays. What is the next step? Add both products together! Twenty plus fifteen equals thirty-five. What is the final step? Check your answer by finding the product of the original equation. Seven times five is thirty-five, so the answer is correct! While Sheriff Squeaks informs Big 'Arry how many squares he has in all, let's review! Remember, to use the distributive property of multiplication, first identify a factor to break down into smaller parts. Next, distribute the other factor to the smaller factors, and solve. Then, add together the two products to get the final product. Finally, check your answer by finding the product of the original problem! "So Big 'Arry, you basically have as many squares as the Lil 'Arry's have put together!" "Woah, what's going on here!" "Imani, you will never believe what I just saw in that virtual reality world!"