How To Do Word Problems In Algebra

Hi, I'm Dr. Shah, I was the National Lecture Competition winner in 1989, and I'm the maths master at Mathscool. Now, ready for a new way of doing math? Word problems in algebra.

So we're 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 kinds of things are a plus in mathematical notation.

Minus, less, difference, less than, below – those sorts of things would be minus sign. Multiply by, product, and of are all multiply by signs. Divide, shared, per would be a divided by sign.

Times itself is another way of saying squared so that would be square. And sometimes, you'll see consecutive numbers. Well, consecutive numbers, if you call the first of our consecutive numbers n, then the second of the consecutive numbers would be n+1.

So n would be an unknown number, and n+1 would be the next number on from there. Similarly instead of saying consecutive numbers, if it said an even number and we didn't know what the even number was, we will call it 2n with the 2 in front of there making sure that it's even because whatever n is, it will be multiplied by 2 to give us an even number. And if we want it an odd number, we would call it 2n+1 making sure from the even, add 1, that will make sure that it's odd.

And if we want it consecutive odd numbers, then if I first saw that number 2n+1, then to get to the next odd number, we'd have to add another 2 to that, so it would be 2n+3, it would be our consecutive odd numbers. You don't have to do it as 2n+1 2n+3, you can also do it as 2n-1 and 2n+1. So in other words subtracting 2 from that 1 to get you our add number.

Okay, so let's move on to some examples where the question is written in English and we have to convert it into mathematical equation before we solve it. Okay, so for our second example, the sum of two consecutive numbers is 53, we have to find the numbers. The sum means plus, and two consecutive numbers, we said before consecutive numbers where one of the numbers might be called n, in which case the other number can be called n+1.

So the sum of two consecutive numbers is, is equals, and then 53. So now, we've converted the question which is now written in English into a mathematical equation. The first thing I'm going to do is simplify the equation, n+n is 2n +1 is 53, and then I'm going to solve it, again using the diagram n x 2 +1 is 53, I need to minus 1 from both sides.

2n is 52, and the opposite of times 2 would be divided by 2. So dividing both sides by 2, we get the n is 26. So n is 26, now n was the first of these numbers.

So n was 26, and that means the next number would be n+1, 27, so the two numbers that are consecutive and added to get me 53 are 26 and 27.