## 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

Ready, Set, Here we go....

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

Step 2: Add 3

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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