Question

vocabulary and concept check

1. writing describe two ways you can use a table to write a proportion.
2. writing what is your first step when solving \\(\frac{x}{15} = \frac{3}{5}\\)? explain.
3. open - ended write a proportion using an unknown value \\(x\\) and the ratio \\(5:6\\). then solve it.

Explanation:

Question 1:

To write a proportion using a table, one way is to organize equivalent ratios in rows or columns. For example, if a table has two quantities with corresponding values, we can check if the ratios of corresponding values are equal (e.g., in a table of miles and hours, check if miles/hours is constant for different rows). Another way is to use the table to identify two pairs of values (e.g., from two rows) and set up a proportion such that the ratio of the first pair equals the ratio of the second pair (e.g., if row 1 has \(a\) and \(b\), row 2 has \(c\) and \(d\), then \(\frac{a}{b}=\frac{c}{d}\) if they are proportional).

Step1: Identify the method to solve the proportion

To solve \(\frac{x}{15}=\frac{3}{5}\), the first step is to use cross - multiplication. Cross - multiplication is based on the property of proportions: if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\).

Step2: Apply cross - multiplication to the given proportion

For the proportion \(\frac{x}{15}=\frac{3}{5}\), applying cross - multiplication, we get \(x\times5=15\times3\). This step is used to convert the proportion into an equation that can be solved for \(x\).

Step1: Write the proportion

We are given the ratio \(5:6\). Let's set up a proportion where one of the ratios is \(5:6\) and the other ratio involves the unknown \(x\). For example, we can write \(\frac{5}{6}=\frac{x}{12}\) (here we choose 12 as the second term of the second ratio arbitrarily, we could choose other numbers too).

Step2: Solve the proportion

Using cross - multiplication on \(\frac{5}{6}=\frac{x}{12}\), we have \(6x=5\times12\).

Step3: Calculate the value of \(x\)

First, calculate \(5\times12 = 60\). Then, solve the equation \(6x = 60\) for \(x\) by dividing both sides of the equation by 6. So, \(x=\frac{60}{6}=10\).

(Another example of a proportion: \(\frac{5}{6}=\frac{10}{x}\). Solving this: cross - multiply to get \(5x = 6\times10 = 60\), then \(x=\frac{60}{5}=12\))

Answer:

1. Organize equivalent ratios in rows/columns (check if corresponding value ratios are equal). 2. Identify two value pairs from the table and set their ratios equal (e.g., \(\frac{\text{value1}}{\text{value2}}\) for two rows are equal in proportion).

Question 2: