\(2 \div \frac13 = {?}\) can be viewed as “how many \(\frac13\)s are in 2?”

Because there are 3 thirds in 1, there are \((2 \boldsymbol\cdot 3)\) or 6 thirds in 2. So dividing 2 by \(\frac13\) has the same outcome as multiplying 2 by 3.
\(2 \div \frac23 = {?}\) can be viewed as “how many \(\frac23\)s are in 2?”

We already know that there are \((2 \boldsymbol\cdot 3)\) or 6 thirds in 2. To find how many \(\frac23\)s are in 2, we need to combine every 2 of the thirds into a group. Doing this results in half as many groups. So \(2 \div \frac23 = (2 \boldsymbol\cdot 3) \div 2\), which equals 3.
\(2 \div \frac43 = {?}\) can be viewed as “how many \(\frac43\)s are in 2?”

Again, we know that there are \((2 \boldsymbol\cdot 3)\) thirds in 2. To find how many \(\frac43\)s are in 2, we need to combine every 4 of the thirds into a group. Doing this results in one fourth as many groups. So \(2 \div \frac43 = (2 \boldsymbol\cdot 3) \div 4\), which equals \(1\frac12\).

Acc6.3 Family Support Material