Write the following fractions in simplest form:
`84/(98)`

Answer

To simplify the fraction \( \frac{84}{98} \), we will follow these steps:

### Step 1: Find the prime factorization of the numerator (84).
- Divide 84 by 2:
\[ 84 \div 2 = 42 \]
- Divide 42 by 2:
\[ 42 \div 2 = 21 \]
- Divide 21 by 3:
\[ 21 \div 3 = 7 \]
- Divide 7 by 7:
\[ 7 \div 7 = 1 \]
- So, the prime factorization of 84 is:
\[ 84 = 2^2 \times 3 \times 7 \]

### Step 2: Find the prime factorization of the denominator (98).
- Divide 98 by 2:
\[ 98 \div 2 = 49 \]
- Divide 49 by 7:
\[ 49 \div 7 = 7 \]
- Divide 7 by 7:
\[ 7 \div 7 = 1 \]
- So, the prime factorization of 98 is:
\[ 98 = 2 \times 7^2 \]

### Step 3: Write the fraction using the prime factorizations.
Now we can write the fraction \( \frac{84}{98} \) as:
\[ \frac{2^2 \times 3 \times 7}{2 \times 7^2} \]

### Step 4: Cancel the common factors.
- The common factors in the numerator and denominator are \( 2 \) and \( 7 \).
- Cancel one \( 2 \) from the numerator and one \( 7 \) from the denominator:
\[ \frac{2 \times 3}{7} \]

### Step 5: Simplify the fraction.
Now we have:
\[ \frac{2 \times 3}{7} = \frac{6}{7} \]

### Final Answer:
The simplest form of the fraction \( \frac{84}{98} \) is:
\[ \frac{6}{7} \]

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