Michigan League of Academic Games

~Double Divide (Dividing Fractions)~ (All Levels)

A great old strategy! Use it to multiply numbers together within your equation~ without using any multiplication operation! Double divide can be used to set a small goal (it takes 5 cubes, minimum) or as a solution or piece of a solution. First read through the mathematical concept, then look to the end for the shortcut

It works through the principle of dividing fractions, and that’s not nearly as frightening as it may sound:

3 ÷ (1 ÷ 2) = 6

* Note the parenthesis if you play basic, as order of operations need apply!

(1 ÷ 2) = ½

This gives you 3 ÷ ½

When dividing fractions, take the reciprocal (flip the fraction over!), and change the operation from divide to mulitiply:

3 x 2/1 You are taking the opposite of division (multiplication) and therefore you need
the opposite of the fraction~ so flip it around)

Any whole number can be written as a fraction by placing it over 1:

3 = 3/1 So our new equation is written as: 3/1 x 2/1

From here, just multiply the numerators and the denominators:

3 x 2 = 6 and 1 x 1= 1 (6 / 1)

Last, divide the numerator by the denominator: 6÷1 = 6

SUPER SECRET SHORTCUT:

3 ÷ (1÷ 2) = x

Multiply the two ‘outside’ numbers, here 3 and 2.
Divide by the ‘inside’ number, here 1.

3 x 2 ÷ 1 = 6

Try these:

4 ÷ (2 ÷ 3) =

(2+3) ÷ (1 ÷ 5) =

7 ÷ (3 ÷ 9) =

4 + (6 ÷ (2 ÷ 3)) =

Special thanks to Natalie Durkee of Ann Arbor Angell for this lesson.

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