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Determine if each pair of ratios is equivalent or not.

[tex]\[

\frac{9}{10} \quad \frac{32}{40}

\][/tex]

[tex]\(\neq\)[/tex]

Answer :

To determine if the pair of ratios [tex]\(\frac{9}{10}\)[/tex] and [tex]\(\frac{32}{40}\)[/tex] are equivalent, let's follow the steps below:

1. Simplify Each Ratio to Decimal Form

- First, convert [tex]\(\frac{9}{10}\)[/tex] into a decimal:
[tex]\[
\frac{9}{10} = 0.9
\][/tex]

- Next, convert [tex]\(\frac{32}{40}\)[/tex] into a decimal:
[tex]\[
\frac{32}{40} = 0.8
\][/tex]

2. Compare the Decimals

Now, compare the decimal values:
- For [tex]\(\frac{9}{10}\)[/tex], we have [tex]\(0.9\)[/tex].
- For [tex]\(\frac{32}{40}\)[/tex], we have [tex]\(0.8\)[/tex].

3. Determine if the Ratios are Equivalent

Ratios are equivalent if their decimal forms are the same. In this case:
- [tex]\(0.9\)[/tex] is not equal to [tex]\(0.8\)[/tex].

Therefore, the ratios [tex]\(\frac{9}{10}\)[/tex] and [tex]\(\frac{32}{40}\)[/tex] are not equivalent.

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