Express the following ratios in their simplest form :
`85 : 170 `

Answer

To express the ratio \( 85 : 170 \) in its simplest form, we will follow these steps:

### Step 1: Write the ratio as a fraction
The given ratio \( 85 : 170 \) can be expressed as a fraction:
\[ \frac{85}{170} \]

### Step 2: Simplify the fraction
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator.

Both 85 and 170 are divisible by 5. Let's divide both by 5:
\[ \frac{85 \div 5}{170 \div 5} = \frac{17}{34} \]

### Step 3: Simplify further if possible
Now, we check if \( 17 \) and \( 34 \) can be simplified further. The number \( 34 \) is also divisible by \( 17 \):
\[ \frac{17 \div 17}{34 \div 17} = \frac{1}{2} \]

### Step 4: Write the simplified ratio
Since the question asks for the ratio, we convert the fraction back into ratio form:
\[ 1 : 2 \]

Thus, the simplest form of the ratio \( 85 : 170 \) is:
\[ \boxed{1 : 2} \]

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