Question

Answer numbers 1-4 with work please

Answer 1

`\large\boxed{Q1.\ 6(1)/(4)\ cups}\\\boxed{Q2.\ 3(1)/(3)\ pounds}\\\boxed{Q3.\ 72:64=9:8}\\\boxed{Q4.\ 32:64=12:24}`

Explanation:

In Q1 and Q2 we must make the proportion.

`Q1.\\s-\text{number of cups of sugar}\\\\(2(1)/(2))/((2)/(5))=(s)/(1)\to s=2(1)/(2):(2)/(5)=(2\cdot2+1)/(2)\cdot(5)/(2)=(5)/(2)\cdot(5)/(2)=(25)/(4)=6(1)/(4)`

`Q2.\\p-\text{number of pounds of mashed potatoes}\\\\(2(4)/(6))/((4)/(5))=(p)/(1)\to p=2(4)/(6):(4)/(5)=(2\cdot6+4)/(6)\cdot(5)/(4)=(16\!\!\!\!\!\diagup^4)/(6)\cdot(5)/(4\!\!\!\!\diagup_1)=(20)/(6)=(20:2)/(6:2)=(10)/(3)=3(1)/(3)`

`Q3.\\\\72:64=(72)/(64)=(72:8)/(64:8)=(9)/(8)=9:8\\\\\text{Other method}\\\\72:64=9:x\to(72)/(64)=(9)/(x)\qquad\text{cross multiply}\\\\72x=(64)(9)\qquad\text{divide both sides by 72}\\\\x=(576)/(72)\\\\x=8`

`Q4.\\\\32:x=12:24\\\\(32)/(x)=(12)/(24)\qquad\text{cross multiply}\\\\12x=(32)(24)\qquad\text{divide both sides by 12}\\\\x=(768)/(12)\\\\x=64`