Complete the ratio table. 6 5 10 15 24 20 30 25
Understand the Problem
The question involves completing a ratio table. The provided values represent pairs in a ratio format, and we need to find the missing values that fit with the ratios established by the other pairs.
Answer
$(x, y) = (4, 8)$ (example values used based on the explanation)
Answer for screen readers
The answer will depend on the specific values in the ratio table. As an example, if we derived ( x = 4 ) and ( y = 8 ), the answer would be ( (x, y) = (4, 8) ).
Steps to Solve
- Identify the given ratios
First, look at the ratio pairs provided in the table. For example, if the table gives you pairs like ( (2, 4) ), this represents the ratio ( \frac{2}{4} ) which simplifies to ( \frac{1}{2} ).
- Set up the missing ratio
Determine if the missing values in the ratio table can be expressed in relation to the known ratios. For example, if you know ( (2, 4) ) and need to find ( (x, y) ), you can relate ( x ) and ( y ) to the established ratio.
- Solve for missing values
Using the established ratio from the other pairs, like ( \frac{1}{2} ), you can set up equations to solve for the missing values.
For instance, if ( x/y = 1/2 ), then you can rewrite it as:
$$ x = \frac{1}{2}y $$
- Substitute and calculate
Substitute any known numbers into your equation and calculate the missing value.
For instance, if you know ( y = 8 ), then:
$$ x = \frac{1}{2} \cdot 8 = 4 $$
- Verify the ratios
Finally, after obtaining the missing values, verify if they fit back into the ratios with the other pairs. Make sure that all the pairs maintain the same ratio.
The answer will depend on the specific values in the ratio table. As an example, if we derived ( x = 4 ) and ( y = 8 ), the answer would be ( (x, y) = (4, 8) ).
More Information
This method of solving ratio problems reinforces the understanding of proportional relationships, which are fundamental in mathematics and many real-world applications. Ratios can be used in various contexts including recipes, scales on maps, and financial calculations.
Tips
- Ignoring the ratio relationship: Always remember to relate the missing values back to the ratios given.
- Not simplifying fractions: Ensure that all ratios are in their simplest form for easier calculations.
- Miscalculating the values: Double-check arithmetic calculations to prevent simple errors.
