How do you write 175% as a fraction, mixed number, or whole number in simplest form?
The Correct Answer and Explanation is:
To convert 175% into a fraction in its simplest form, we follow a systematic approach. Percent means “per hundred,” so 175% can be expressed as:
[
175\% = \frac{175}{100}
]
Next, we simplify the fraction (\frac{175}{100}). To do this, we need to find the greatest common divisor (GCD) of the numerator (175) and the denominator (100). The factors of each number help us identify the GCD.
Finding the GCD:
- The prime factorization of 175 is:
- 175 = 5 × 5 × 7 = (5^2 \times 7)
- The prime factorization of 100 is:
- 100 = 2 × 2 × 5 × 5 = (2^2 \times 5^2)
The common factor in both factorizations is (5^2) (or 25). Therefore, the GCD of 175 and 100 is 25.
Simplifying the Fraction:
Now, we divide both the numerator and denominator by the GCD (25):
[
\frac{175 \div 25}{100 \div 25} = \frac{7}{4}
]
So, in fraction form, 175% is equal to (\frac{7}{4}).
Converting to a Mixed Number:
To express (\frac{7}{4}) as a mixed number, we divide 7 by 4. The quotient is 1 with a remainder of 3. Thus, we can write:
[
\frac{7}{4} = 1 \frac{3}{4}
]
Conclusion:
175% can be expressed as a fraction (\frac{7}{4}) or as a mixed number (1 \frac{3}{4}). This conversion is useful in many mathematical contexts, especially when needing to perform calculations involving percentages in their simplest forms. Expressing percentages in fraction or mixed number form often clarifies relationships between values, making further mathematical operations easier to execute.