Division of Fraction

Start with $$9\ \frac{3}{5}$$ because that is the total amount that the dispenser can hold. Also, you will take the $$\frac{3}{10}$$ groups away from the $$9\ \frac{3}{5}$$ .

Since $$3\ \frac{1}{3}$$ is the total amount of dog food, the division expression should start with $$3\ \frac{1}{3}$$ . In addition, since you need $$\frac{2}{3}$$ cup each day, that is the divider, the divisor, what you use to repeatedly subtract, use $$\frac{2}{3}$$ after the division symbol.

In this word problem, since each serving represents $$\frac{7}{8}$$ , it should be the divisor (after the division sign) because that's the amount going into each group. The total amount to make the servings from is $$\frac{3}{8}$$ because that is the total amount that you have to make your $$\frac{7}{8}$$ serving groups.

What you are making groups of is the divisor, the second number, the number to be divided.

In this word problem, since each serving represents $$\frac{5}{8}$$ , it should be the divisor (after the division sign) because that's the amount going into each group. The total amount to make the servings from is $$\frac{3}{8}$$ which is why the problem says in $$\frac{3}{8}.$$

The story problem "How many $$\frac{2}{9}$$ -meter pieces of rope can you cut from a piece that is $$\frac{2}{3}$$ meter long?" best represents $$\frac{2}{3}\div\frac{2}{9}$$ because $$\frac{2}{3}$$ is the total amount that you have to start with. In the problem, we see the word from, showing we need to start with the $$\frac{2}{3}$$ . Also, you are making groups of the divisor, the number after the division symbol, and the number to be divided. In this word problem, that is $$\frac{2}{9}$$ meter pieces.

Both models start with 4 because that is the total amount to be divided. Then, make groups of $$\frac{2}{3}$$ back to zero. To get the total amount of groups/the quotient, count the total groups of $$\frac{2}{3}$$ between 4 and 0. Both models show there are 6 groups of $$\frac{2}{3}$$ in 4.