1875/10000 as a simplified mixed number
The Correct Answer and Explanation is :
The correct answer is: 0 \frac{3}{16}
To simplify the fraction ( \frac{1875}{10000} ) into a mixed number, we first simplify it to its lowest terms.
Step 1: Find the GCD
The greatest common divisor (GCD) of 1875 and 10000 needs to be calculated. We can use the prime factorization method:
- Factor 1875:
- Divide by 5: ( 1875 \div 5 = 375 )
- Divide by 5: ( 375 \div 5 = 75 )
- Divide by 5: ( 75 \div 5 = 15 )
- Divide by 5: ( 15 \div 5 = 3 )
- Finally, ( 3 \div 3 = 1 ) So, the prime factorization of 1875 is:
[
1875 = 5^4 \times 3^1
]
- Factor 10000:
- Divide by 10: ( 10000 \div 10 = 1000 )
- Divide by 10: ( 1000 \div 10 = 100 )
- Divide by 10: ( 100 \div 10 = 10 )
- Divide by 10: ( 10 \div 10 = 1 ) Thus, the prime factorization of 10000 is:
[
10000 = 10^4 = (2 \times 5)^4 = 2^4 \times 5^4
]
Step 2: Find the GCD
The GCD is the product of the lowest powers of all prime factors present in both numbers:
- For ( 5 ): The minimum power is ( 5^4 ).
- For ( 3 ) and ( 2 ): They do not appear in both factorizations.
Thus, the GCD of 1875 and 10000 is ( 5^4 = 625 ).
Step 3: Simplify the Fraction
Now divide both the numerator and denominator by their GCD:
[
\frac{1875 \div 625}{10000 \div 625} = \frac{3}{16}
]
Step 4: Convert to Mixed Number
The fraction ( \frac{3}{16} ) is less than 1, so it remains as it is. However, to express this as a mixed number, we see that:
- There are no whole parts (as ( 3 < 16 )), so we can express it simply as ( 0 \frac{3}{16} ).
Final Answer
Thus, the simplified mixed number for ( \frac{1875}{10000} ) is:
[
0 \frac{3}{16}
]
In conclusion, when simplifying fractions, finding the GCD is essential, and once simplified, fractions can be expressed as mixed numbers if they are improper (greater than or equal to one). In this case, our result remained a proper fraction.