## Math Tricks Explained "The Math Behind the Magic"

Ever wondered how a certain math trick works? Me too! On this page you'll get math tricks explained so you can understand the math behind the magic!

So why did I decide to write a page that takes some of the mystery out of it. Well, since this site is all about helping students enjoy and learn math, showing a student why, can sometimes motivate them to explore even more!

And besides....,knowing the magic behind the math, builds their math confidence! So if the person you do this trick on is 12 years old, here's how it would work:

Step 1: 1 x 5 = 5 (Multiply 1st digit of age by 5)

Step 2: 5 + 3 = 8 (Add 3 to this result)

Step 3: 8 x 2 = 16 (Multiply by 2)

Step 4: 16 + 2 = 18 (Add the 2nd digit of age)

Step 5: 18 – 6 = 12 (Subtract 6)

And there you have it…..the age of person is 12.

### How it Works

So now think algebra with me.

In algebra, we use letters to take the place of numbers. So in our example, the person is 12 years old. The first number of their age, we will call x. And the second number of their age, we will call y. So for our example, x is 1 and y is 2.

Ok, now for a little more algebra.

Using algebra, any person's age can be represented by,

10x + y

Before I explain how the math trick works, I want to convince you that 10x + y can represent a person's age. So let's try some examples to make sure I'm telling you the truth (:

Example 1: 12 years old

x = 1

y = 2

10x + y = 10(1) + 2 = 10 + 2 = 12

See, it worked, right!

Example 2: 25 years old

x = 2

y = 5

10x + y = 10(2) + 5 = 20 + 5 = 25

### Now to explain the trick....

Step 1: Multiply 1st digit of age by 5

5x

5x + 3

Step 3: Multiply by 2

2(5x + 3)

Step 4: Add the 2nd digit of age

2(5x + 3)+ y

Step 5: Subtract 6

2(5x + 3)+ y - 6

Ok, now we'll do a little algebra.

2(5x + 3)+ y - 6 = 10x + 6 + y - 6 = 10x + y

And that is the person's age.

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