Question

Write each ratio in simplest form1- 300:1082- 5280:8003- 42:1204- 20:965- 24:16

Answer 1

Given:

1) 300:108

`\begin{gathered} (300)/(108) \\ \text{Greatest common factor of 300 and 108 is 12.} \\ (300)/(108)=(25\cdot12)/(9\cdot12)=(25)/(9)\Rightarrow25\colon9 \end{gathered}`

2) 5280:800

`\begin{gathered} (5280)/(800) \\ \text{Greatest common factor of 5280 and 800 is 160.} \\ (5280)/(800)=(33\cdot160)/(5\cdot160)=(33)/(5)\Rightarrow33\colon5 \end{gathered}`

3) 42:120

`\begin{gathered} (42)/(120) \\ \text{Greatest common factor of 42 and 120 is 6.} \\ (42)/(120)=(7\cdot6)/(20\cdot6)=(7)/(20)\Rightarrow7\colon20 \end{gathered}`

4) 20:96

`\begin{gathered} (20)/(96) \\ \text{Greatest common factor of 20 and 96 is 4.} \\ (20)/(96)=(4\cdot5)/(4\cdot24)=(5)/(24)\Rightarrow5\colon24 \end{gathered}`

5)

`\begin{gathered} (24)/(16) \\ \text{Greatest common factor of 24 and 16 is 8.} \\ (24)/(16)=(3\cdot8)/(2\cdot8)=(3)/(2)\Rightarrow3\colon2 \end{gathered}`