Express each of the following ratios in simplest form :
2.1 : 1.2

Answer

To express the ratio 2.1 : 1.2 in its simplest form, follow these steps:

### Step 1: Write the ratio as a fraction
We start by converting the ratio into a fraction:
\[ \frac{2.1}{1.2} \]

### Step 2: Eliminate the decimal points
To eliminate the decimal points, we can multiply both the numerator and the denominator by 10 (since both numbers have one decimal place):
\[ \frac{2.1 \times 10}{1.2 \times 10} = \frac{21}{12} \]

### Step 3: Find the prime factors of both numbers
Next, we find the prime factorization of both the numerator and the denominator:
- The prime factorization of 21 is:
\[ 21 = 3 \times 7 \]
- The prime factorization of 12 is:
\[ 12 = 2 \times 2 \times 3 = 2^2 \times 3 \]

### Step 4: Cancel the common factors
Now, we can cancel the common factor of 3 from both the numerator and the denominator:
\[ \frac{21 \div 3}{12 \div 3} = \frac{7}{4} \]

### Step 5: Write the simplest form of the ratio
Thus, the simplest form of the ratio 2.1 : 1.2 is:
\[ 7 : 4 \]

### Final Answer
The simplest form of the ratio 2.1 : 1.2 is **7 : 4**.

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