Distributive Property of Multiplication

Big 'Arry seems upset, it looks like Detective Squeaks is needed! "Big 'Arry! What seems to be the problem?" “Help! I don't know how many squares I have in total, but apparently, the Little 'Arry's can help!" Let's help Detective Squeaks calculate how much Big 'Arry has altogether by using the distributive property of multiplication. The distributive property of multiplication is sometimes called the distributive law of multiplication. It teaches us that one factor can be broken down into two smaller factors, to solve a multiplication problem by breaking down one factor, or number, into smaller parts. We can multiply them separately then add the products together to find the same product as if we had multiplied the original two factors together. The distributive property of multiplication is very useful, because it allows bigger multiplication problems to be broken down into smaller ones! Let's practise 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, multiply each number by the factor outside the brackets, this is four. We need to find four times three, twice. 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 Detective Squeaks calculate how many squares Big 'Arry has in total! Big 'Arry is an array of seven by five, so set up an array with seven rows of five! What is the next step? Break down one of the factors! Let's break down the larger of the two factors, seven. How can we break down the seven? We can break the seven into four plus three. What is the next step? Multiply both numbers by the factor outside the brackets, which is five. 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! Whilst Detective Squeaks tells Big 'Arry how many squares he has in total, let's review! Remember, to use the distributive property of multiplication, first identify a factor to break down into smaller parts. Next, multiply both smaller factors by the larger factor and solve. Then, add together the two products to get the total. Finally, check your answer by finding the product of the original problem! "So Big 'Arry, you basically have as many squares as the Little '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!"