What is the reduced fraction form of 175%?
The correct answer and explanation is :
To express 175% as a fraction in its simplest form, follow these steps:
Step 1: Understand what a percentage is
A percentage is simply a number out of 100. The symbol “%” means “per hundred.” Thus, 175% can be written as:
[
175\% = \frac{175}{100}
]
Step 2: Simplify the fraction
Next, simplify the fraction (\frac{175}{100}). To do this, find the greatest common divisor (GCD) of 175 and 100. The GCD is the largest number that divides both 175 and 100 without leaving a remainder.
- The factors of 175 are: 1, 5, 7, 25, 35, 175.
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
The greatest common divisor of 175 and 100 is 25.
Step 3: Divide both the numerator and denominator by the GCD
Now, divide both the numerator (175) and the denominator (100) by their GCD, which is 25:
[
\frac{175}{100} = \frac{175 \div 25}{100 \div 25} = \frac{7}{4}
]
Step 4: Final Answer
Thus, the fraction form of 175% is:
[
\frac{7}{4}
]
This is the simplified fraction form of 175%.
Explanation
We begin by converting the percentage into a fraction, recognizing that the percentage symbol represents “out of 100.” After converting, we simplify the fraction by finding the greatest common divisor of the numerator and the denominator. The GCD is used to divide both the numerator and denominator, resulting in the simplest form of the fraction. In this case, dividing both 175 and 100 by 25 gives the reduced fraction (\frac{7}{4}), which is the simplest form of the percentage 175%.
If you wanted to express this as a mixed number, you could divide 7 by 4, which gives:
[
\frac{7}{4} = 1 \frac{3}{4}
]
Therefore, 175% is equivalent to the fraction (\frac{7}{4}) or the mixed number (1 \frac{3}{4}).