Question

find the number that makes the ratio equivalent to 1:2.
5:□

Explanation:

Step1: Understand equivalent ratios

Equivalent ratios are like equivalent fractions—they have the same relationship between the two numbers. For a ratio \(a:b\) and another ratio \(c:d\) to be equivalent, \(\frac{a}{b}=\frac{c}{d}\). Here, we know one ratio is \(1:2\) (so \(\frac{1}{2}\)) and the other ratio is \(5:\square\) (so \(\frac{5}{x}\), where \(x\) is the unknown number).

Step2: Set up the proportion

We set up the proportion \(\frac{1}{2}=\frac{5}{x}\). To solve for \(x\), we can cross - multiply. Cross - multiplying means multiplying the numerator of the first fraction by the denominator of the second fraction and setting it equal to the denominator of the first fraction multiplied by the numerator of the second fraction. So, \(1\times x = 2\times5\).

Step3: Solve for x

Simplifying the right - hand side of the equation \(1\times x=2\times5\), we get \(x = 10\).

Answer:

10