# Question 25def

Dec 1, 2017

$5$ wins to $7$ losses is the better season record.

#### Explanation:

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

$\setminus \frac{\textcolor{red}{5}}{\textcolor{b l u e}{7}} \setminus \quad , \setminus \quad \setminus \frac{\textcolor{b l u e}{7}}{\textcolor{red}{9}}$

Multiply diagonal terms:

$\textcolor{red}{5} \setminus \cdot \textcolor{red}{9} \setminus \quad , \setminus \quad \textcolor{b l u e}{7} \cdot \textcolor{b l u e}{7}$

Evaluate:

$\textcolor{red}{45} \setminus \quad , \setminus \quad \textcolor{b l u e}{49}$

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

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

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

Dec 6, 2017

$7 : 9$ is a better season

#### Explanation:

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: $\text{ "5 : 7" "and " "7 : 9" }$ is the same as
$\textcolor{w h i t e}{\times \times \times x . \times} \downarrow \textcolor{w h i t e}{\times \times \times \times \times} \downarrow$
$\textcolor{w h i t e}{\times \times \times . \times} \times 7 \text{ "and " } \times 5$
$\textcolor{w h i t e}{\times \times \times x . \times} \downarrow \textcolor{w h i t e}{\times \times \times \times \times} \downarrow$
$\textcolor{w h i t e}{\times \times \times . \times} 35 : 49 \text{ "and" } \textcolor{b l u e}{35 : 45}$

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

OR

Comparing: $\text{ "5 : 7" "and " "7 : 9" }$ is the same as
$\textcolor{w h i t e}{\times \times \times x . \times} \downarrow \textcolor{w h i t e}{\times \times \times \times \times} \downarrow$
$\textcolor{w h i t e}{\times \times \times . \times} \times 9 \text{ "and " } \times 7$
$\textcolor{w h i t e}{\times \times \times x . \times} \downarrow \textcolor{w h i t e}{\times \times \times \times \times} \downarrow$
$\textcolor{w h i t e}{\times \times \times . \times} 45 : 63 \text{ "and" } \textcolor{b l u e}{49 : 63}$

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%#