Write 9/12 as a decimal and as
a percent. Describe two ways to find the
answer.
The Correct Answer and Explanation is :
To express 9/12 as both a decimal and a percent, we begin by simplifying the fraction and then converting it into both forms.
Step 1: Simplify the Fraction
The fraction 9/12 can be simplified by dividing both the numerator (9) and the denominator (12) by their greatest common divisor (GCD), which is 3.
[
\frac{9}{12} = \frac{9 ÷ 3}{12 ÷ 3} = \frac{3}{4}
]
Step 2: Convert to a Decimal
To convert a fraction into a decimal, you can divide the numerator by the denominator. In this case, divide 3 by 4:
[
3 ÷ 4 = 0.75
]
Thus, 9/12 as a decimal is 0.75.
Step 3: Convert to a Percent
To convert a decimal to a percent, multiply the decimal by 100.
[
0.75 × 100 = 75\%
]
Thus, 9/12 as a percent is 75%.
Explanation of Two Methods to Solve
Method 1: Division Method
You can directly convert the fraction to a decimal by dividing the numerator by the denominator. For 9/12, divide 9 by 12:
[
9 ÷ 12 = 0.75
]
Once you have the decimal, multiply by 100 to convert it to a percentage:
[
0.75 × 100 = 75\%
]
Method 2: Simplification Method
Simplify the fraction before converting it. As shown earlier, 9/12 simplifies to 3/4. Then, use known fraction-to-decimal conversions. Since 3/4 is a common fraction, we know:
[
\frac{3}{4} = 0.75
]
This makes converting to a decimal easier. From there, multiply by 100 to get the percentage.
Both methods give the same results, but simplifying first can make the calculation quicker.