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%#