Model of the quotient of 1/2 divided by 1/6

Question

evaluate the quotient of 1/2 divided by 1/6 using model

Answer 1

The question can be stated: how many sixths make a half?

If x sixths make a half then x/6=1/2. Since 6 is 3 times 2: 1/2=3×1/(3×2)=3/6, (multiplying the top and bottom of 1/2 by 3), so 3/6=x/6, making x=3.

The picture shows a long rectangle divided into sixths, six equal boxes. You can see that three of the boxes make up half the length of the rectangle, so the picture is a model of the question.