Write the ratio 12 : 9 as an equivalent ratio of 4 : x.
To find an equivalent ratio, we need to find the value of x that makes the two ratios equal.
We have the ratio 12 : 9 and we want to express it as the ratio 4 : x.
To find the value of x, we can set up a proportion:
12/9 = 4/x
To solve for x, we can cross-multiply:
12*x = 9*4
12x = 36
Dividing both sides by 12, we find:
x = 3
So the equivalent ratio is 4 : 3.
To find an equivalent ratio, we need to find the value of x in the ratio 4 : x, where the ratio 12 : 9 is equal to 4 : x.
Using cross-multiplication, we set up the equation:
12/9 = 4/x
Now, we can solve for x by cross-multiplying:
12 * x = 4 * 9
12x = 36
Dividing both sides of the equation by 12, we can solve for x:
x = 36 / 12
x = 3
Therefore, the equivalent ratio of 12 : 9 as the ratio 4 : x is 4 : 3.
To find the value of x in the equivalent ratio 4 : x, we need to determine the relationship between the terms of the given ratio 12 : 9 and the ratio 4 : x.
The given ratio is 12 : 9. To simplify this ratio, we can divide both terms by their greatest common divisor (GCD). In this case, the GCD of 12 and 9 is 3.
Dividing both terms of the ratio 12 : 9 by 3, we get:
12 ÷ 3 : 9 ÷ 3
4 : 3
Therefore, the equivalent ratio to 12 : 9 is 4 : 3.
Now, we need to find the value of x in the ratio 4 : x. Since the two ratios are equivalent, the relationship between their corresponding terms should remain the same. In other words, the relationship between the first term and the second term of each ratio should remain constant.
In the given ratio 12 : 9, the relationship between the first term and the second term is 12 ÷ 9, which simplifies to 4 ÷ 3.
In the ratio 4 : x, we want to find the value of x that maintains the same relationship between the first term 4 and the second term x. Therefore, the relationship is 4 ÷ x.
Since the relationship between the first terms in both ratios is the same (4 ÷ 3), we can equate the relationship between the second terms:
4 ÷ 3 = 4 ÷ x
To find x, we can cross-multiply:
4 * x = 4 * 3
4x = 12
Finally, we can solve for x by dividing both sides of the equation by 4:
x = 12 ÷ 4
x = 3
Therefore, the equivalent ratio to 12 : 9 as a ratio of 4 : x is 4 : 3.