Question

÷ 2/3 = 0
5 2 ÷ 4/9

Explanation:

First Problem (assuming the first problem is \( x \div \frac{2}{3} = 6 \) to solve for \( x \)):

Step1: Recall division inverse operation

To solve for \( x \) in \( x \div \frac{2}{3}=6 \), we know that dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the left - hand side as \( x\times\frac{3}{2} \). The equation becomes \( x\times\frac{3}{2}=6 \).

Step2: Solve for \( x \)

To isolate \( x \), we multiply both sides of the equation by the reciprocal of \( \frac{3}{2} \), which is \( \frac{2}{3} \). So \( x = 6\times\frac{2}{3} \). Calculating \( 6\times\frac{2}{3} \), we can simplify: \( 6\) and \( 3\) cancel out, \( 6\div3 = 2 \), then \( 2\times2=4 \). So \( x = 4 \).

Second Problem (\( 2\div\frac{4}{9} \)):

Step1: Use division - fraction rule

Dividing by a fraction \( \frac{a}{b} \) (where \( a = 4 \), \( b = 9 \)) is equivalent to multiplying by its reciprocal \( \frac{b}{a} \). So \( 2\div\frac{4}{9}=2\times\frac{9}{4} \).

Step2: Simplify the multiplication

We can simplify \( 2\times\frac{9}{4} \). The number \( 2 \) and the denominator \( 4 \) have a common factor of \( 2 \). \( 2\div2 = 1 \), \( 4\div2 = 2 \). So the expression becomes \( 1\times\frac{9}{2}=\frac{9}{2}=4.5 \) (or \( 4\frac{1}{2} \)).

Answer:

s:
For the first problem (solving \( x\div\frac{2}{3}=6 \)): \( \boldsymbol{4} \)
For the second problem (\( 2\div\frac{4}{9} \)): \( \boldsymbol{\frac{9}{2}} \) (or \( \boldsymbol{4.5} \) or \( \boldsymbol{4\frac{1}{2}} \))