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A candle maker has 4 1/2 pounds of clear wax. He wants to cut the wax into pieces that are 2/3 pound each. How many 2/3 pound pieces can he divide the wax into. How much wax does he have leftover

Respuesta :

[tex]\bf \cfrac{4\frac{1}{2}}{\quad \frac{2}{3}\quad }\implies \cfrac{\frac{4\cdot 2+1}{2}}{\quad \frac{2}{3}\quad }\implies \cfrac{\frac{9}{2}}{\quad \frac{2}{3}\quad }\implies \cfrac{9}{2}\cdot \cfrac{3}{2}\implies \cfrac{27}{4}\implies 6\frac{3}{4} \\\\\\ \textit{so, 6 whole pieces, and }\frac{3}{4}\textit{ of another one}[/tex]

now, what's the leftover?  well, 3/4 of the last one, namely 3/4 of 2/3, what is 3/4 of 2/3 anyway?  well, is just their product,

[tex]\bf \cfrac{\underline{3}}{4}\cdot \cfrac{2}{\underline{3}}\implies \cfrac{2}{4}\implies \stackrel{lbs}{\cfrac{1}{2}}[/tex]
boffeemadrid

The number of pieces of wax and the leftover amount is required.

The number of pieces of the required mass will be 6.

[tex]\dfrac{1}{2}\ \text{pound}[/tex] of wax will be leftover.

The amount of clear wax is [tex]4\dfrac{1}{2}\ \text{pounds}[/tex]

The mass of required piece is [tex]\dfrac{2}{3}\ \text{pounds}[/tex]

The number of pieces will be

[tex]\dfrac{4\dfrac{1}{2}}{\dfrac{2}{3}}\\ =\dfrac{\dfrac{9}{2}}{\dfrac{2}{3}}\\ =\dfrac{27}{4}\\ =6\dfrac{3}{4}[/tex]

The number of pieces of the required mass will be 6.

[tex]\dfrac{3}{4}\ \text{pieces}[/tex] will remain.

[tex]\dfrac{3}{4}\times \dfrac{2}{3}=\dfrac{1}{2}\ \text{pound}[/tex]

[tex]\dfrac{1}{2}\ \text{pound}[/tex] of wax will be leftover.

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