Determine if one, both, or neither of the following is a proportion. 16/8=24/12, 8/4=12/6
To determine if a statement is a proportion, we need to check if the ratios on both sides of the equation are equal.
For the first statement, we have:
16/8 = 24/12
This can be simplified to:
2 = 2
Since both sides are equal, this statement is a proportion.
For the second statement, we have:
8/4 = 12/6
This can be simplified to:
2 = 2
Again, both sides are equal, so this statement is also a proportion.
Therefore, both of the given statements are proportions.
To determine if the given equations are proportions, we need to check if the ratios on both sides are equal.
Let's analyze each equation separately:
Equation 1: 16/8 = 24/12
We can simplify both sides of this equation by dividing the numerator and denominator of each fraction by their greatest common divisor (GCD). In this case, the GCD is 8:
16/8 = 24/12
2/1 = 3/2
Since the left-hand side (LHS) and the right-hand side (RHS) fractions are not equal, this equation is NOT a proportion.
Now, let's move on to the second equation:
Equation 2: 8/4 = 12/6
Again, we can simplify both sides of the equation by dividing the numerator and denominator of each fraction by their GCD, which is 4:
8/4 = 12/6
2/1 = 3/1
In this case, the LHS and the RHS fractions are equal. Therefore, this equation IS a proportion.
To summarize:
Equation 1 (16/8 = 24/12) is NOT a proportion.
Equation 2 (8/4 = 12/6) IS a proportion.
To determine if a given equation is a proportion, we need to check if the fractions on both sides of the equation are equal.
Let's analyze the first equation 16/8 = 24/12:
To get started, we need to simplify both sides of the equation.
16/8 can be simplified as follows:
16/8 = 2 * 8 / 8 = 2
Similarly, 24/12 can be simplified as:
24/12 = 2 * 12 / 12 = 2
Now that both sides have been simplified, we can see that the equation can be written as:
2 = 2
Since both sides of the equation are equal, we can conclude that the first equation 16/8 = 24/12 is a proportion.
Let's move on to analyze the second equation 8/4 = 12/6:
Again, we need to simplify both sides of the equation:
8/4 simplifies to:
8/4 = 2
12/6 simplifies to:
12/6 = 2
Now, let's look at the equation:
2 = 2
Once again, both sides of the equation are equal. Therefore, we can conclude that the second equation 8/4 = 12/6 is also a proportion.
To summarize, both of the given equations are proportions.