4,590.72 m
<h3>
Further explanation</h3>
<u>Given:</u>
A clothing factory uses 1,275.2 meters of clothes a week to make shirts.
<u>Question:</u>
How much cloth is needed to make 3³/₅ times many shirts?
<u>The Process:</u>
Let us prepare a model for the use of clothes a week to make shirts.
![\boxed{1,275.2} \rightarrow in \ meters](https://tex.z-dn.net/?f=%5Cboxed%7B1%2C275.2%7D%20%5Crightarrow%20in%20%5C%20meters)
Let us do multiplication on a fraction at first.
![\boxed{ \ = \frac{3}{5} \times 1,275.2 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%20%5Cfrac%7B3%7D%7B5%7D%20%5Ctimes%201%2C275.2%20%5C%20%7D)
![\boxed{ \ = 3 \times \frac{1}{5} \times 1,275.2 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%203%20%5Ctimes%20%5Cfrac%7B1%7D%7B5%7D%20%5Ctimes%201%2C275.2%20%5C%20%7D)
![\boxed{ \ = 3 \times \frac{1,275.2}{5} \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%203%20%5Ctimes%20%5Cfrac%7B1%2C275.2%7D%7B5%7D%20%5C%20%7D)
![\boxed{ \ = 3 \times 255.04 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%203%20%5Ctimes%20255.04%20%5C%20%7D)
![\boxed{\boxed{ \ 765.12 \ }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%20%5C%20765.12%20%5C%20%7D%7D)
Then we make a model for how much cloth is needed to make 3³/₅ (three and three fifths) times many shirts. Recall that ![\boxed{3\frac{3}{5} \ parts = 3 \ parts + \frac{3}{5} \ parts}](https://tex.z-dn.net/?f=%5Cboxed%7B3%5Cfrac%7B3%7D%7B5%7D%20%5C%20parts%20%3D%203%20%5C%20parts%20%2B%20%5Cfrac%7B3%7D%7B5%7D%20%5C%20parts%7D)
![\boxed{1,275.2}\boxed{1,275.2}\boxed{1,275.2}\boxed{765.12}](https://tex.z-dn.net/?f=%5Cboxed%7B1%2C275.2%7D%5Cboxed%7B1%2C275.2%7D%5Cboxed%7B1%2C275.2%7D%5Cboxed%7B765.12%7D)
Finally, let us calculate how much cloth is needed to make 3³/₅ times many shirts.
![\boxed{ \ = (1,275.2 \times 3) + 765.12 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%20%281%2C275.2%20%5Ctimes%203%29%20%2B%20765.12%20%5C%20%7D)
![\boxed{ \ = 3825.6 + 765.12 \ }](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5C%20%3D%203825.6%20%2B%20765.12%20%5C%20%7D)
![\boxed{\boxed{ \ 4,590.72 \ meters \ }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%20%5C%204%2C590.72%20%5C%20meters%20%5C%20%7D%7D)
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Keywords: a clothing factory, uses 1,275.2 meters, clothes, a week, to make shirts, how much, cloth is needed, to make 3 3/5 times, parts, model, multiplication, fraction