Question

Dear Mitch, 

Do you know any tricks for the seven times table?  They are the ones I'm bad at remembering.  And I figured I would ask you because I read your tricks for other numbers and they really helped. 

Think, you must know something for sevens.

From Tony 

Redford, MI

Answer

Dear Tony, 

There are plenty of ways you can remember most of the sevens in the times table, and I have given a bunch of them in previous answe4rs to questions like yours.  But since it's been a while, I'll repeat a few of the ideas that people seemed to like best, and then I'll tell you a new thought. 

First, some ideas I must have mentioned before:

Since sevens seem to be the group that most students find the trickiest to memorize, people have developed all kinds of helping ideas, and here's one of my favorites:  Turn the problem around and use whatever trick you know for the other number in the question.  For example, if you are trying to figure out what seven times nine is, say to yourself "nine times seven".  Then you can use the famous finger trick that works for all the nines (check out the archive of questions and answers on this site and you will find it, or type in nine times table trick with fingers and you will also find it here or on someone else's site.)  Another example is nine times ten.  What do you do?  Say ten times nine and you know how easy the trick is for the tens.  And recall the mnemonics I gave; for example, seventh heaven is an expression some adults use to mean total happiness.  And some adults say it when they finally make it to bed after a long, hard day.  They may say "I am in seventh heaven for the night".  That sounds like seven-seven-for-nine.  Indeed, 7 x 7 = 49. Seventh heaven for the night. (7 7 49...) 

But here's a better idea:  When all else fails, use mathematical concepts. For seven, remember that when you multiply a number by another number, the result is equal to the result you get when you break one of the factors (the numbers being multiplied by each other) into two parts that add up to the whole number you started with, and then adding the results together.  For example, with seven, break it up into 2 + 5.

So, when you have to figure out what seven times six is, for example, try doing this: 

7 = 5 + 2,

So,

   6   x        7      =

 6     x    (5 + 2) = 

(6 x 5) + (6 x 2) =

   30      + 12     =

     42 

And that works because 6 x 7 does equal 42!

The reason I like this method for the sevens is that seven can always be broken up into 2 + 5, and students usually find the twos and the fives to be among the easiest ones to learn.  Then you just add up the two smaller answers.

 One more example:

    7        x    8   = 

(5 + 2 )  x    8   =

(5 x 8) +  (2 x 8) =

    40    +     16   = 

           56

And that is correct, because 7 x 8 does = 56 !! 

Hope this helps,

Mitch