# Fraction Concentration

## Instructions

Fraction Concentration is a concentration game with a twist. You aren't looking for cards that look the same...you are looking for cards with the same *value*. The game can be played as a two person game, or a single person can play the game alone, in order to practice recognizing equivalent fractions.

### Object of the Game

To find pairs of fractions in the grid which are equivalent.

### Game Instructions

Click on any two squares to flip those squares and reveal the fractions. If the fractions are equivalent (for example, 1/3 and 2/6, or 3/7 and 9/21), after a couple seconds the squares will disappear, and a point will be added to the player's score. If not, the fractions will be hidden again, and the other player's turn begins. Note: any time a player correctly identifies a pair of equivalent fractions, the player gets another turn.

Play continues until all the squares are removed.

### Equivalent Fractions

In case you need a reminder, equivalent fractions are fractions which have the same value. Let's say you have a pie, and you cut it into four pieces. If you take two pieces, that's 2/4 of the pie (two pieces out of four). But if the pie was cut into *eight* pieces, how many pieces would you have to take to have the*same amount*? Well, each piece is half as big, so you would need *twice* as many pieces. So four pieces out of eight is the same amount as two pieces out of four. In other words, 2/4 = 4/8.

Notice that in the fraction 4/8, the numerator (the top number) is twice the numerator of the first fraction, and the denominator (the bottom number) is twice the value of the denominator of the first fraction. This is how you can find out if two fractions are equivalent; if you can multiply both the numerator and denominator by the same number, and get the numerator and denominator of the second fraction, they are equivalent.

Example: Look at the fractions 3/7 and 9/21. What do you have to multiply 3 by to get 9? Three, right? So now multiply 7 (the denominator of the first fraction) by three. What do you get? Twenty-one! And that's the denominator of the second fraction. So the two are equal.

Another example: What about 2/5 and 8/15? Well, if you multiply 2 by 4, you get eight. So now try multiplying the denominator (5) by 4. Uh oh. You don't get fifteen, you get *twenty*! So these fractions aren't equivalent.