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Writing Proportions

A proportion is a mathematical comparison between two ratios.

A ratio is a comparison between two numbers.

For instance, the ratio of apples to bananas in a fruit basket is 1 apple to 2 bananas:

  • [tex]\dfrac{1\hspace{3}apple}{2\hspace{3}bananas}[/tex]

This is proportional to the ratio of apples to bananas in another fruit basket, which is 2 apples to 4 bananas:

  • [tex]\dfrac{2\hspace{3}apples}{4\hspace{3}bananas}[/tex]

To write a proportion from this information, we can compare the ratios by makign them equal to each other:

  • [tex]\dfrac{1\hspace{3}apple}{2\hspace{3}bananas}=\dfrac{2\hspace{3}apples}{4\hspace{3}bananas}[/tex]
  • [tex]\dfrac{1}{2}=\dfrac{2}{4}[/tex]

Solving the Question

We're given:

  • $118 per week
  • $472 per 4 weeks
  • These are proportional

$118 per week is one ratio:

  • [tex]\dfrac{118\hspace{3}dollars}{1\hspace{3}week}[/tex]

$472 per 4 weeks is another ratio:

  • [tex]\dfrac{472\hspace{3}dollars}{4\hspace{3}weeks}[/tex]

Now, set them equal to each other to create a proportion:

  • [tex]\dfrac{118\hspace{3}dollars}{1\hspace{3}week}=\dfrac{472\hspace{3}dollars}{4\hspace{3}weeks}\\\\\dfrac{118}{1}=\dfrac{472}{4}[/tex]

Answer:

Therefore, the proportion is [tex]\dfrac{118}{1}=\dfrac{472}{4}[/tex].