Question #25def

We can simply express both ratios as fractions, then cross multiply to see which one is larger.

`\frac{color(red)(5)}{color(blue)(7)}\quad,\quad\frac{color(blue)(7)}{color(red)(9)}`

Multiply diagonal terms:

`color(red)(5)\cdot color(red)(9)\quad,\quad color(blue)(7)cdot color(blue)(7)`

Evaluate:

`color(red)(45)\quad,\quad color(blue)(49)`

The blue color is larger, so we look for the fraction whose numerator is blue.

That’s `\frac{7}{9}`, so that ratio is larger than `\frac{5}{7}`.

Therefore, `5` wins to `7` losses is less, and thus a better record.

You can campare ratios by making one of the two numbers the same.

Remember you can multiply or divide a ratio by any value, as long as you do the same to all the values.

Comparing: `" "5 : 7" "and " "7 : 9" "` is the same as
`color(white)(xxxxxxx.xx)darr color(white)(xxxxxxxxxx)darr`
`color(white)(xxxxxx.xx)xx7" "and " "xx5`
`color(white)(xxxxxxx.xx)darr color(white)(xxxxxxxxxx)darr`
`color(white)(xxxxxx.xx)35:49" "and" "color(blue)(35:45)`

Now we can compare them. `35` wins for `45` losses is better than `35` wins and `49` losses.

OR

Comparing: `" "5 : 7" "and " "7 : 9" "` is the same as
`color(white)(xxxxxxx.xx)darr color(white)(xxxxxxxxxx)darr`
`color(white)(xxxxxx.xx)xx9" "and " "xx7`
`color(white)(xxxxxxx.xx)darr color(white)(xxxxxxxxxx)darr`
`color(white)(xxxxxx.xx)45:63" "and" "color(blue)(49:63)`

Now compare them. `49` wins for `63` losses is better than `45` wins and `63` losses.

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You could also calculate the difference between the wins and losses as a percentage of the wins. In each case the number of losses was `2` more than the wins.

`2/5 xx 100%" "and" "2/7 xx100%`

`40%" compared with "28.6%`