 # Multiplied and Divided

MIGHTY MULTIPLICATION

Multiplication is nothing more than a shortcut to addition. Let’s say you have five baskets with apples, and each basket contains seven apples. If all you know is addition, you will have to do the following problem: 7 + 7 + 7 + 7 + 7. Or, if you know how to multiply, you can just do 7 x 5. Either way, you will get the same number of apples.

Multiplying on Your Fingers

Here’s a trick you can try with your friends-show them how to multiply by nine on your fingers. Hold your hands out in front of you. Then follow the following example.

To multiply 4 x 9, bend down the fourth finger from the left. The number of fingers to the left of the bent finger represent the “tens” digit and the number of fingers to the right represent the “ones” digit, so the answer is 36. This trick works up to 9 x 9 = 81.

To Multiply 9 by Any Digit Can you figure out how the finger multiplication trick works? Here is another way to look at it-try to multiply 9 x 6:

The “tens” digit: 6 – 1 = 5 The “ones” digit: 9-5 = 4 Therefore, 9 x 6 = 54. Right?

Russian Peasant Multiplication

In Russia, peasants used to use an interesting technique for multiplication-halving, doubling, and adding numbers. When you have two numbers that you need to multiply, keep doubling one as you divide the other in halves (ignore any remainders or fractions). If the number in the halved column is odd (including the original value), mark the doubled number for addition later. At the end, add all the marked doubled numbers. Sounds complicated? It will make a lot more sense with an example. Let’s take 22 X 44.

Positive and Negative Numbers

. you learned how to add and subtract positive and negative numbers. But what about multiplication? Do the same rules apply? Actually, they don’t. In fact, the number line method doesn’t work for multiplication. Instead, it might be helpful to imagine a video of a person who is walking backward and forward. People can walk backward and forward, and the video cam be played forward or rewound:

Walking forward is a positive action. Walking backward is a negative action. Film running forward is positive. Film running backward is negative.

Imagine that you videotape your friend walking forward. If you watch it on video played forward, you will see your friend walking forward. This represents multiplying two positive numbers: (+) x (+) = +. Now, if you rewind the tape, your friend will seem to be walking backward: (+) X (-) = –