Another way proof $1/2-1/3=1/6$ by using picture?

Question

We know that $\dfrac{1}{2} -\dfrac{1}{3} =\dfrac{1}{6}$. I proved it by picture What is (are) another way (ways) by using picture?

Answer 1

This is a nice picture, using an equilateral triangle, because the shape has both 2-way and 3-way symmetry. Each large right triangle is 1/2, and each kite is 1/3.

Is this the kind of thing you were looking for?

Answer 2

The assertion is true in any commutative ring where the multiplicative inverses exist, even though you can't always draw a picture.

$1/a$ is the solution to the equation $ax = 1$ so

$$ 6 \left( \frac{1}{2} - \frac{1}{3} \right) = 2 \times 3 \times \left( \frac{1}{2} \right) - 2 \times 3 \times\left( \frac{1}{3} \right) = 3 - 2 = 1 $$ so the expression on the left in the question is the multiplicative inverse of $6$.

(This is the core of the rule for adding fractions.)

Answer 3

I think that an other useful picture could be the disk. We can divide in two pieces the disk, of course at 180° and in the same way we can divide it in 3 pieces at 120°. At this point is simple to show what remains, and also the computation of the difference.

Answer 4

Primary school teachers generally use pattern blocks.

Show that the green [1/6] plus the blue [1/3] equals the red [1/2].