Determine if each pair of ratios creates equivalent unit rates or not.

Ratios:

1. [tex]$\frac{1}{4}$[/tex] and [tex]$\frac{5}{20}$[/tex]

2. [tex]$\frac{3}{4}$[/tex] and [tex]$\frac{18}{20}$[/tex]

3. [tex]$\frac{2}{5}$[/tex] and [tex]$\frac{12}{15}$[/tex]

Equivalent or Non-equivalent:

1. _ Equivalent _ Non-equivalent

2. _ Equivalent _ Non-equivalent

3. _ Equivalent _ Non-equivalent

Sure, let's determine if each pair of ratios create equivalent unit rates or not.

1. Ratios [tex]$\frac{1}{4}$[/tex] and [tex]$\frac{5}{20}$[/tex]

To check if these two ratios are equivalent, we can simplify them both to their simplest forms:

[tex]\[
\frac{5}{20} = \frac{5 \div 5}{20 \div 5} = \frac{1}{4}
\][/tex]

Since both simplify to [tex]$\frac{1}{4}$[/tex], these two ratios are equivalent.

2. Ratios [tex]$\frac{3}{4}$[/tex] and [tex]$\frac{18}{20}$[/tex]

Again, we simplify both ratios to their simplest forms:

[tex]\[
\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]

The ratio [tex]$\frac{3}{4}$[/tex] does not simplify further and remains [tex]$\frac{3}{4}$[/tex]. Since [tex]$\frac{3}{4} \neq \frac{9}{10}$[/tex], these two ratios are not equivalent.

3. Ratios [tex]$\frac{2}{5}$[/tex] and [tex]$\frac{12}{15}$[/tex]

Simplify both ratios to their simplest forms:

[tex]\[
\frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5}
\][/tex]

The ratio [tex]$\frac{2}{5}$[/tex] does not simplify further and remains [tex]$\frac{2}{5}$[/tex]. Since [tex]$\frac{2}{5} \neq \frac{4}{5}$[/tex], these two ratios are not equivalent.

So, the final determination is:

- [tex]$\frac{1}{4}$[/tex] and [tex]$\frac{5}{20}$[/tex] are equivalent.
- [tex]$\frac{3}{4}$[/tex] and [tex]$\frac{18}{20}$[/tex] are not equivalent.
- [tex]$\frac{2}{5}$[/tex] and [tex]$\frac{12}{15}$[/tex] are not equivalent.