35/8 simplified? Explain
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{35}{8} ), we need to determine if it can be reduced to a simpler form. Here’s how we can go about it:
- Identify the Greatest Common Divisor (GCD): The first step in simplifying a fraction is to find the GCD of the numerator (35) and the denominator (8). The GCD is the largest number that divides both numbers without leaving a remainder.
- For 35, its factors are 1, 5, 7, and 35.
- For 8, its factors are 1, 2, 4, and 8.
- The only common factor between 35 and 8 is 1.
Since the GCD is 1, the fraction ( \frac{35}{8} ) cannot be simplified further.
- Convert to a Mixed Number (if desired): Sometimes, it is more helpful to express improper fractions (where the numerator is greater than the denominator) as mixed numbers. To convert ( \frac{35}{8} ) into a mixed number:
- Divide the numerator (35) by the denominator (8):
[
35 \div 8 = 4 \quad \text{(whole number)}
] - Multiply the whole number (4) by the denominator (8):
[
4 \times 8 = 32
] - Subtract this product from the numerator (35) to find the remainder:
[
35 – 32 = 3
] - This gives us a mixed number of ( 4 \frac{3}{8} ).
- Final Answer: Therefore, the simplified form of ( \frac{35}{8} ) is ( \frac{35}{8} ) (since it cannot be simplified), and as a mixed number, it can be expressed as ( 4 \frac{3}{8} ).
In conclusion, ( \frac{35}{8} ) is already in its simplest form, and understanding how to convert it into a mixed number can provide a clearer representation of the value.