Explaination

Alejandra’s average equals 227 ÷ 5 = 45.4. Nigel’s average equals 189 ÷ 5 = 37.8. The difference is 7.6.
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We can save a bit of time by recognizing the following fraction property: \(\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}\)

Here's what I mean:

Alejandra took five Spanish quizzes and scored a total of 227 points.
Alejandra's average = \(\frac{277}{5}\)

Nigel took the same quizzes and scored a total of 189.
Nigel's average = \(\frac{189}{5}\)

What is the difference between Alejandra’s average score and Nigel’s average score?

Difference = \(\frac{227}{5}-\frac{189}{5}\)

\(=\frac{227-189}{5}\) [after we apply the above fraction property]

\(=\frac{38}{5}\)

\(= 7.6\)

ASIDE: The video below shows how to quickly divide by 5 in your head

Answer: 7.6

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