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How To Solve Word Problems In Algebra
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Hi, I am Doctor Shah. I was the national lecturer competition winner in 1989 and I am the maths master at Mathscool. Now, ready for new word in math. With word problems in algebra, so we are going to learn to convert the English in a word problem into maths. So if you see "is", "am" , "are" that would be an "equal" sign in mathematical notation. "And", "sum", "greater than", "longer", "heavier", those kind of things are a "plus" in mathematical notation. "Minus", "less", "difference", "less than", "below" those sort of things would be a "minus" sign. "Multiply by", "product" and "of" are all "multiply by" signs. "Divide" , "share", "per" would be a "divide by" sign. "Times itself" is another way of saying "squared" so that would be square and sometimes you will see consecutive numbers, well, consecutive numbers if we call the first of our consecutive numbers "n" then the second of the consecutive numbers would be "n plus one". So "n" would be an unknown number and "plus one" would be the next number onward from that. Similarly if it said, instead of saying consecutive numbers, if it said an even number and we did not know what the even number was, we will call it "two n", the "two" in front of it making sure that it is even because whatever n is, it will be multiplied by two to give us an even number and if we wanted an odd number we would call it "two n plus one" make it even add one that will ensure it is odd and if we wanted consecutive odd numbers, then if I first saw the number was "two n plus one" then to get to the next odd number we have to add another two to that to be "two n plus three" it would be our consecutive odd numbers. You don't have to do as "two n plus one", "two n plus three" you can also do it as "two n minus one" and "two n plus one" so, in other words subtracting two from that to get the odd number. So, lets move on to some examples where the question is in English and we have to convert it into mathematical equation before we can solve that. So, this is a typical question where we have got to convert the wordy question into maths before we can solve that. I think of a number multiply it by two, add six and divide the answer by three. This gives ten, we have to find the original number. So, this original number that we don't know of, is our unknown number. So we are going to call that "x", so starting with x, multiply it by two, so I will put a "two" in front of it that is multiplied it by two, add six, plus six and divide the answer by three, divide by three and this gives ten so this gives means "equals" ten. OK So I have converted the question which was wordy into an algebric equation which I can just now solve using my flow diagram method so "x" next to the "x" is a times two then there is a plus six and then lastly there is a divide by three, before I get to the equal sign, equals ten so the first thing I want to do is get rid of the "divided by three" which is "times three" so that and that cancel out, on the left hand side I am left with "two x plus six" and here I get three times ten is thirty opposite of the plus six is subtract six so I am going to subtract six from both sides and so that gives me "two x" is thirty subtract six is twenty four and then my last step is to divide by two both sides. I have run out at the bottom there so I just carry on up here "two x" is twenty four divide by two divide by two that is the opposite of the times two and that should take me back to the x. So the times two and the divide by two cancel each other out I get "x" is twelve and there is my answer.
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