Question

determine if the one both or neither of the following is a proportion 16/8 =? 24/12, 8/4 =? 12/6

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if a proportion is true or false, we need to simplify both sides of the equation and check if they are equal.

For the first proportion, 16/8 = 24/12:

Simplifying 16/8, we get: 2
Simplifying 24/12, we get: 2

Since both sides simplify to the same value of 2, this proportion is true.

For the second proportion, 8/4 = 12/6:

Simplifying 8/4, we get: 2
Simplifying 12/6, we get: 2

Once again, both sides simplify to the same value of 2, so this proportion is true.

Therefore, both of the given proportions are valid.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine if a proportion is true, we need to check if the ratios on each side of the equation are equal.

First equation: 16/8 = 24/12
Step 1: Simplify both ratios.
16/8 = 2/1
24/12 = 2/1
Step 2: Compare the simplified ratios.
2/1 = 2/1
The ratios are equal.

Second equation: 8/4 = 12/6
Step 1: Simplify both ratios.
8/4 = 2/1
12/6 = 2/1
Step 2: Compare the simplified ratios.
2/1 = 2/1
The ratios are equal.

So, both of the given equations are proportions.

Answer 3

[AI-generated answer — Explain Bot]

To determine if the given pairs of fractions are proportions, we need to check if they are equivalent to each other. We can do this by simplifying each fraction to its simplest form.

Let's analyze the first pair: 16/8 and 24/12.

To simplify 16/8, we divide both the numerator and the denominator by their greatest common divisor (GCD), which is 8. Dividing both 16 and 8 by 8, we get:

16 ÷ 8 = 2
8 ÷ 8 = 1

Therefore, 16/8 simplifies to 2/1.

Now, let's simplify 24/12. By dividing both 24 and 12 by their GCD, which is 12, we find:

24 ÷ 12 = 2
12 ÷ 12 = 1

Hence, 24/12 simplifies to 2/1.

Since both 16/8 and 24/12 simplify to the same fraction, 2/1, we can conclude that the first pair, 16/8 and 24/12, is a proportion.

Moving on to the second pair: 8/4 and 12/6.

When we simplify 8/4 by dividing both 8 and 4 by their GCD, which is 4, we obtain:

8 ÷ 4 = 2
4 ÷ 4 = 1

So, 8/4 simplifies to 2/1.

Similarly, 12/6 can be simplified by dividing both 12 and 6 by their GCD, which is 6. Dividing, we find:

12 ÷ 6 = 2
6 ÷ 6 = 1

Hence, 12/6 simplifies to 2/1.

Just like the first pair, the second pair, 8/4 and 12/6, simplifies to the same fraction, 2/1. Therefore, the second pair is also a proportion.

In summary:
- The pair 16/8 and 24/12 is a proportion since both fractions simplify to 2/1.
- The pair 8/4 and 12/6 is also a proportion since both fractions simplify to 2/1.