[size=150]To make sense of the question “How many [math]\frac{2}{3}[/math]s are in 1?,” Andre wrote equations and drew a tape diagram.[/size][br][br][math]?\cdot\frac{2}{3}=1[/math] [math]1\div\frac{2}{3}=?[/math] [br] 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[/img][br][br]In an earlier task, we used pattern blocks to help us solve the equation [math]1\div\frac{2}{3}=?[/math]. Explain how Andre’s tape diagram can also help us solve the equation.
How many [math]\frac{3}{4}[/math]s are in 1?
How many [math]\frac{2}{3}[/math]s are in 1?
How many [math]\frac{3}{2}[/math]s are in 1?
How many [math]\frac{3}{8}[/math]-inch thick books make a stack that is 6 inches tall?
How many groups of [math]\frac{1}{2}[/math]pound are in [math]2\frac{3}{4}[/math]pounds?
Write a question that can be represented by the division equation [math]5\div1\frac{1}{2}=?[/math].
Find the answer to the previous question. Explain or show your reasoning.