How do you write 120% as a fraction, mixed number, or whole number in simplest form

The Correct Answer and Explanation is:

To express 120% as a fraction, mixed number, or whole number in its simplest form, we need to follow a few mathematical steps:

Step 1: Convert the percentage to a fraction

A percentage represents a number out of 100, so 120% can be written as:
[
\frac{120}{100}
]

Step 2: Simplify the fraction

Now, we simplify the fraction. To do this, we find the greatest common divisor (GCD) of 120 and 100. The GCD of 120 and 100 is 20, so we divide both the numerator and the denominator by 20:
[
\frac{120 \div 20}{100 \div 20} = \frac{6}{5}
]
So, 120% as a fraction in simplest form is:
[
\frac{6}{5}
]

Step 3: Convert the improper fraction to a mixed number

An improper fraction is one where the numerator is larger than the denominator. To convert (\frac{6}{5}) into a mixed number, we divide 6 by 5:
[
6 \div 5 = 1 \text{ remainder } 1
]
This means that (\frac{6}{5}) can be written as:
[
1 \frac{1}{5}
]
So, 120% as a mixed number is:
[
1 \frac{1}{5}
]

Step 4: Convert to a whole number (if applicable)

In this case, since the fraction (\frac{6}{5}) is greater than 1, it cannot be expressed as a whole number. However, if you were to round 120% to the nearest whole number, it would round to 120, which is the original percentage expressed as a whole number.

Final Answer:

As a fraction: (\frac{6}{5})
As a mixed number: (1 \frac{1}{5})
As a whole number: 120 (if rounded)

Explanation:

The process involves converting the percentage into a fraction, simplifying it, and then converting it into a mixed number if needed. It’s important to recognize that 120% is greater than 100%, which is why it results in a fraction greater than 1, and in mixed number form, it shows one whole and an additional part.