Question

think about 6 ÷ \frac{2}{3}. how can you find the number of \frac{2}{3}s in 6? step 1: multiply 6 by 3 to find the number of thirds in 6. step 2: divide by 2 to find the number of groups of 2 thirds. which expression means to multiply 6 by 3, then divide by 2? $6 \div \frac{2}{3} = 6 \times \\, ?$

Explanation:

Step1: Recall the rule of dividing by a fraction

When dividing by a fraction $\frac{a}{b}$ (where $a,b
eq0$), we use the rule $c\div\frac{a}{b}=c\times\frac{b}{a}$. Here, $c = 6$, $a = 2$, and $b = 3$, so $6\div\frac{2}{3}=6\times\frac{3}{2}$.

Step2: Analyze the given steps

The problem says we first multiply 6 by 3 (to find the number of thirds in 6) and then divide by 2 (to find the number of groups of $\frac{2}{3}$). Mathematically, this is equivalent to $6\times3\div2$, which can be rewritten as $6\times\frac{3}{2}$ (since dividing by 2 is the same as multiplying by $\frac{1}{2}$, and $3\times\frac{1}{2}=\frac{3}{2}$). So the missing number in the box is $\frac{3}{2}$.

Answer:

$\frac{3}{2}$