How do you write 4 is to 16 as 12 is to 48 as a proportion in fractional notation? Do not simply your answer.
To write the proportion "4 is to 16 as 12 is to 48" in fractional notation without simplifying, we can write:
\[ \frac{4}{16} = \frac{12}{48} \]
To write the proportion "4 is to 16 as 12 is to 48" in fractional notation without simplifying, we can follow these steps:
Step 1: Write the first ratio as a fraction.
4:16 can be written as 4/16.
Step 2: Write the second ratio as a fraction.
12:48 can be written as 12/48.
Step 3: Set up the proportion using the fractions.
4/16 = 12/48.
Thus, the proportion in fractional notation is 4/16 = 12/48.
To write the proportion "4 is to 16 as 12 is to 48" in fractional notation, we need to express the ratios as fractions.
First, let's write the first ratio "4 is to 16" as a fraction. The ratio means that there are 4 parts to every 16 parts. So we can write it as 4/16.
Second, let's write the second ratio "12 is to 48" as a fraction. This ratio means that there are 12 parts to every 48 parts. So we can write it as 12/48.
Now, we have both ratios as fractions: 4/16 and 12/48. To show that they are equivalent, we need to find a common factor that can be used to simplify both fractions.
To simplify fractions, we can divide both the numerator and denominator of each fraction by their greatest common factor (GCF).
Let's calculate the GCF for both fractions. The prime factors of 4 are 2 * 2. The prime factors of 16 are 2 * 2 * 2 * 2. These fractions share a GCF of 4.
So, we divide the numerator and denominator of 4/16 by 4, resulting in 1/4.
Now, let's calculate the GCF for the second fraction. The prime factors of 12 are 2 * 2 * 3. The prime factors of 48 are 2 * 2 * 2 * 2 * 3. These fractions share a GCF of 12.
So, we divide the numerator and denominator of 12/48 by 12, resulting in 1/4.
Now, we have both fractions simplified: 1/4 and 1/4.
The final proportion in fractional notation is 4/16 = 12/48 = 1/4.