Question

What the lowest term for 720/8100

Answer 1

To get to the lowest term:

First, let's check if we can divide both numbers by two:

`\begin{gathered} 720\text{ is divisible by 2}\rightarrow(720)/(2)=360 \\ 8100\text{ is divisible by 2}\rightarrow(8100)/(2)=4050 \\ \text{Therefore,} \\ (720)/(8100)\rightarrow(360)/(4050) \end{gathered}`

Both 360 and 4050 still are divisible by two. Thus,

`\begin{gathered} (360)/(2)\rightarrow180 \\ (4050)/(2)\rightarrow2025 \\ \text{Therefore,} \\ (720)/(8100)\rightarrow(360)/(4050)\rightarrow(180)/(2025) \end{gathered}`

2025 is no longer divisible by 2. Therefore, we move on and check if we can divide both numbers by 3:

`\begin{gathered} 180\text{ is divisible by 3}\rightarrow(180)/(3)\rightarrow60 \\ 2025\text{ is divisible by 3}\rightarrow(2025)/(3)\rightarrow675 \\ \text{Therefore,} \\ (720)/(8100)\rightarrow(360)/(4050)\rightarrow(180)/(2025)\rightarrow(60)/(675) \end{gathered}`

Both 60 and 675 still are divisible by 3. Thus,

`\begin{gathered} (60)/(3)\rightarrow20 \\ (675)/(3)\rightarrow225 \\ \text{Therefore,} \\ (720)/(8100)\rightarrow(360)/(4050)\rightarrow(180)/(2025)\rightarrow(60)/(675)\rightarrow(20)/(225) \end{gathered}`

20 is no longer divisible by 3. And if we try with 4, we get that 225 is not divisible by 4. Let's try with 5

`\begin{gathered} 20\text{ is divisible by 5}\rightarrow(20)/(5)\rightarrow4 \\ 225\text{ is divisible by 5}\rightarrow(225)/(5)\rightarrow45 \\ \text{Therefore,} \\ (720)/(8100)\rightarrow(360)/(4050)\rightarrow(180)/(2025)\rightarrow(60)/(675)\rightarrow(20)/(225)\rightarrow(4)/(45) \end{gathered}`

Notice we can't simplify any further.

Thus, the lowest term for 720/8100 is:

`(4)/(45)`