Reduce the following fractions to simplest form :
`150/350`

Answer

To reduce the fraction \( \frac{150}{350} \) to its simplest form, follow these steps:

### Step 1: Identify the fraction
We start with the fraction:
\[ \frac{150}{350} \]

### Step 2: Cancel out the common zeros
Both the numerator and the denominator have a common factor of 10, which can be simplified by canceling out the zeros:
\[ \frac{150 \div 10}{350 \div 10} = \frac{15}{35} \]

### Step 3: Factor the numerator and denominator
Next, we factor both the numerator and the denominator:
- The numerator \( 15 \) can be factored as \( 5 \times 3 \).
- The denominator \( 35 \) can be factored as \( 5 \times 7 \).

So we rewrite the fraction:
\[ \frac{15}{35} = \frac{5 \times 3}{5 \times 7} \]

### Step 4: Cancel the common factors
Now, we can cancel the common factor of \( 5 \) from both the numerator and the denominator:
\[ \frac{5 \times 3}{5 \times 7} = \frac{3}{7} \]

### Step 5: Check for further simplification
Now we check if \( 3 \) and \( 7 \) have any common factors. Since \( 3 \) and \( 7 \) are both prime numbers and do not have any common factors other than \( 1 \), we conclude that:
\[ \frac{3}{7} \]
is in its simplest form.

### Final Answer:
The simplest form of the fraction \( \frac{150}{350} \) is:
\[ \frac{3}{7} \]

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