Multiply 39 by 41?

Answer 1

11 year old says 1599, but they're so much better at maths.

Answer 2

The answe is 1599, with quite a few ways of reaching this.

Firstly, there's the 'schoolboy' method: 9x1=9, record the 9. 3x1=3, 9x4=36, 3+36=39, record the 9 & carry the 3. 3x4=12, add the carried 3 to make 15. There are no more digits to be found, so you record he '15' and see the full answer as 1599.

My favourite method for this kind of task uses the rule of 'difference of two squares'. Here's how it works:

(X+Y)x(X-Y) = X^2-Y^2. This can be shown using the 'FOIL' (First, Outside, Inside, Last) method of multiplying bracketed terms. XxX = X^2, Xx(-Y) = -XY, YxX = XY, and Yx(-Y) = -Y^2.

Using this little snippet means you can take the average of the two numbers (add them together & divide by 2), find the square of this number, then subtract the square of the difference between the average & either of the two original numbers. This is because the average is your 'X' in this case and the difference is your 'Y'.

39+41=80, and 80/2 = 40. You can now use either 40-39 = 1 or 41-40 = 1. We now thus have X=40 and Y=1.

The square of 40 is easy to calculate as 40 is 4x10 (i.e. 4 followed by a single zero); the square is thus 4x4 x 10x10 (i.e. followed by two zeros) - thus 1600. The square of 1 is even easier, since anything multiplied by1 is itself - and so 1x1 = 1.

We now have to subtract 1 from 1600 (as per X^2 - Y^2). 1600-1 = 1599, and this final answer is one with which we are already faniliar.

Another way is to say that 39x4 = 156. add a zero to make 1560, then 39x1 = 39, add this to make 1599. The alternative here would be 3x41 = 123, add a zero to make 1230, then 9x41 = 369 (9 = 10-1, and 410-41 = 369) and add this to make .... again .... 1599.

I hope this helps; please feel free to drop me a line if you'd like me to discuss any aspects of figure-work.

Answer 3

One of the easiest methods to multiply a large sum like 39 x 41 is to first work out 30 x 40 , next do 30 x 1, then multiply 40 x 9 and 9 x 1. As soon as you have worked out the following sums add all the figures up to get to the final answer. So 39 x 41= 1,599. When working out sums use the method you are most comfortable with.

Answer 4

39 * 41 = 1599

Answer 5

39 * 41 = 1599

Answer 6

39*41= (40+1)(40-1) = 40^2-1^2 = 1600 - 1 = 1599

Answer 7

hoestly? how can you not do this? what are teachers doing these days? line up the numbers.
39
x 41
____
39
1560 (indent to line up under the 4: the 0 is there so you dont write it under the wrong column, the 6 comes from 4 x 9 = 36, the 15 comes from 4 x 3 = 12 plus the 3 from 36)
____
1599

Answer 8

1599

Answer 9

column multiplication's easier

39x
41
---
39+
156
-----
1599

Answer 10

One of the easiest ways to do this is:(40 - 1)(40 + 1) = 1600 - 1 = 1599. Thanks for an easy 2 points!