TenMarks teaches you how to apply distributive property.
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In this track, we will learn how to use the Distributive Law or Distributive Properties when it comes to addition, multiplication, etcetera. The first questions ask us to expand the two equations given. So the first question, first part says 5*3+5, we have to expand it. The law that we’re going to use is Distributive Law of Multiplication over Addition. Well, this law says that if I'm distributing multiplication over addition A*B+C which is multiplication over addition right is the same as A*B+A*C. So, if I'm multiplying A with the addition of B+C, I can separate the two out or distribute the two out. So, let’s apply this principle here, 5*3+5, let’s say this is A, this is B and this is C. So in this case, A*B+C which is5*3+5=5*3+A*C is 5*5. This is the expanded version of this particular equation. Let’s do the same for the next one creating a little bit of space. The next one is 12*10-4. This is the same except it is multiplication over subtraction. Instead of adding within the parenthesis, I'm subtracting over parenthesis. So, A*B-C should be the same as A*B-A*C, exactly the same except instead of adding, I'm distributing over subtracting. So, substituting the values A is 12, B is 10, C is 4, A*B-C= or let’s write this down again 12*10-4 equals well A is 12 so 12*10-12*4, this is the expanded version. This is the Distributive Law of Multiplication over Subtraction. Now, let’s come back to the second question. It wants us to find the product using the distributive property that we’ve been taught. So, the first one—5*84, now because this is 5*84, I can easily write this as 5*80+4 right, 84 is the same as 80+4. So, using the Distributive Law of Multiplication over Addition, I should say that this is the same as 5*80+5*4. All I did was distribute over addition which means 5*80 is easy for me to do mentally which is 400 and 5*4 is 20 so the final answer is 420. Let’s create the space and do the next one which is 4*58. 4*58 can also be written as four times—well instead of 58 I can write 16-2. So, 4*16-2 is the same as 4*60-4*2 which is the same as 4*60 is 240-4*2 is 8 and 240-8 is 232. So, we use the distributive property to make it easy to multiply numbers without actually going through long multiplications.