To solve for the following proportion, you could use equivalent ratios, divide out the known ratio, or use cross products. Choose one of these methods to solve for t. Show your work and explain why you chose that method.
18/5 = 4/t
I learned the cross-multiply method over 60 years ago. I can apply it to many types of problems.
18/5 = 4/t
18t = 20
t = 20/18 = 1 2/18 = 1 1/9
To solve the proportion 18/5 = 4/t, you have the option to use equivalent ratios, divide out the known ratio, or use cross products. Let's explore each method and analyze which one will be the most appropriate in this particular case.
1. Equivalent ratios: To solve for t using equivalent ratios, you would multiply both sides of the equation by the same value. In this case, you would multiply both sides by t. However, this method might not be the most efficient choice because it involves multiplying both sides by an unknown variable, which can sometimes lead to more complex calculations.
2. Divide out the known ratio: To solve for t by dividing out the known ratio, you would divide both sides of the equation by the known ratio, which is 4. This method simplifies the equation by removing the known value on one side of the equation. However, it requires dividing, which might result in decimals or fractions, making the calculation less straightforward.
3. Cross products: To solve for t using cross products, you would multiply the numerator of the left side (18) by the denominator of the right side (t) and set it equal to the product of the numerator of the right side (4) multiplied by the denominator of the left side (5). This creates an equation that can be solved algebraically. Using this method converts the proportion into a simple equation involving multiplication, which can be easier to work with.
Let's choose the cross products method to solve for t:
18 * t = 4 * 5
After multiplying both sides, the equation becomes:
18t = 20
Now we can solve for t by dividing both sides by 18:
t = 20/18
Simplifying the right side gives us:
t = 10/9
Therefore, t equals 10/9 when solving the proportion 18/5 = 4/t using the cross products method. This method was chosen because it directly converts the proportion into a simple equation involving multiplication, making it easier to solve.