Tips, Tricks, and Shortcuts -- 9s

The Correspondent

Everybody else probably knows this already, but because I'm slow to learn and don't test well, I'm going to post it so I'll have it in print to refer back to when it's time to teach the boys these things.

The number 9 might seem like a mathematical troublemaker, but there are a number of very simple tricks and shortcuts that make 9 one of the easiest numbers to deal with.


Adding a single digit to a 9:
Simply subtact 1 from the other addend and add a 10 to it.

The idea is that it's easier to add with a 10, so you change the 9 to a 10 by borrowing 1 from the other number.
For example, 9 + 8 ... Subtract 1 from the 8 to make a 7, then add that 1 to the 9 to make a 10. You've just changed 9 + 8 to 10 + 7. The sum of both is 17.

The kids do this quickly in their heads by thinking, "9 + 6 ... The 6 becomes a 5, and I add a 10 to make 15."


Subtracting 9 from a number in the teens (11, 12, 13, 14, 15, etc.):
Add the two digits together that make up the teen number, and that's the answer.
15 - 9 ... 1 + 5 = 6, so 15 - 9 = 6.
17 - 9 ... 1 + 7 = 8, so 17 - 9 = 8.


Multiplying 9 by 1 through 10:
Place both hands, palms down, an inch or so above a tabletop and spread your fingers.
You'll be counting off numbers by touching one finger at a time to the tabletop, beginning with your left hand pinky, then your left hand ring finger, etc.

To multiply 9 x 4, count "1" and touch your left pinky to the tabletop. Then, lift it and count "2" as you touch your left ring finger to the tabletop. Then, lift it and count "3" as you touch your left middle finger to the tabletop. Lift it and count "4" as you touch your left pointer finger to the tabletop and stop, leaving your pointer finger down -- it'll act as a dividing point.

Count the number of fingers to the left of that dividing point finger (there are 3) and the number of fingers to the right of the dividing point finger (there are 6; don't forget to count your left thumb). There's your answer: 36. 9 x 4 = 36.

Now try 9 x 7 ... When you touch and count 7 fingers, starting from the left, you end up with your right pointer down as a dividing point. There are 6 fingers to the left and 3 fingers to the right. So, 9 x 7 = 63.


Dividing with 9:
When you're faced with a double digit that's evenly divisible by 9 (problems with remainders won't work), the answer is simply one number higher than the first digit of the dividend.

63 divided by 9 = one digit higher than 6 is 7, so 63 divided by 9 = 7.
45 divided by 9 = one digit higher than 4 is 5, so 45 divided by 9 = 5.


Nines made easy!

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