Division by Fractions

Section 7.3
Dividing by a fraction can be thought about as repeated subtraction or sharing equally.

1/2 divided by 3/4 can be read as:

(a) Repeated subtraction: How much of three-fourths are in a half? The answer is 2/3 of 3/4 is in 1/2.
To model this, draw a circle cut in half. Draw the ¾ overlapping one of the halves. You should be able to see that 2/3 of the ¾ are in a half of the circle.

(b) Equal share: If a half is in three-quarters, then how much is in a whole? The answer is 2/3 are in a whole.
To model this, draw a circle cut into quarters. Use a half dozen dots and distribute them equally into three quarters of the circle. You will notice that there are 2 dots in each of the three quarters; therefore using the notion of equal share, there must be 8 dots in a whole circle. Eight dots are 2/3 of a dozen.