ratios what is a ratio? a ratio is a comparison of one quantity to another. for example if i were...

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Ratios What is a ratio? A ratio is a comparison of one quantity to another. For example if I were baking a cake and needed to have one part sugar to four parts flour the ratio would be 1:4 or ¼. DON’T CONFUSE FRACTIONS WITH RATIOS 6.RP Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

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Page 1: Ratios What is a ratio? A ratio is a comparison of one quantity to another. For example if I were baking a cake and needed to have one part sugar to four

Ratios

What is a ratio?A ratio is a comparison of one quantity to

another.

For example if I were baking a cake and needed to have one part sugar to four parts

flour the ratio would be 1:4 or ¼.DON’T CONFUSE FRACTIONS WITH RATIOS

6.RP Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Page 2: Ratios What is a ratio? A ratio is a comparison of one quantity to another. For example if I were baking a cake and needed to have one part sugar to four

The difference between fractions and ratios

• If we were mixing oil for a two cycle engine it might call for a 1:50 ratio. This means for every one part of oil it would be 50 parts gas.

• For the sake of simplicity we will begin with a 1:4 ratio and say that the first number is oil and the second number is gas.

• How is a 1:4 ratio or ¼ different than saying that ¼ (fraction) or 25% of the gas oil mixture is oil?

Page 3: Ratios What is a ratio? A ratio is a comparison of one quantity to another. For example if I were baking a cake and needed to have one part sugar to four

Difference between fractions and ratios continued

• A 1:4 ratio means that there are 5 parts all together and one part is oil. It can be represented by ¼. This is why the context of the problem is important.

¼ as a fraction means that there are 4 parts and 25% of them are oil. If you mixed gas using a fraction model instead of a ratio would you have to much or to little oil in your mixture?

Oil20%

Gas20%

Gas20%

Gas20%

Gas20%

Oil25%

Gas25%

Gas25%

Gas25%

Page 4: Ratios What is a ratio? A ratio is a comparison of one quantity to another. For example if I were baking a cake and needed to have one part sugar to four

Extension

Little Red Riding Hood has a basket that holds eight eggs. 5 of them are brown and 3 are white.

1. What are all the ratios of eggs? Hint: Think about comparing all sets, brown, white and totals.

2. Change all the ratios to fractions, decimals and percentages using a table.

3. What does each decimal or percentage mean in relation to the context?

Page 5: Ratios What is a ratio? A ratio is a comparison of one quantity to another. For example if I were baking a cake and needed to have one part sugar to four

Things to consider

• What mathematical model would help me represent this?

• An area model?• A ratio table?

What is the relationship between between decimals and percentages?

What is the relationship between fractions, decimals and percentages?

Discuss in groups before answering the question. Start with ½. How would you express it as a decimal and fraction? How does this help you to solve the Little Red Riding Hood problem?

Page 6: Ratios What is a ratio? A ratio is a comparison of one quantity to another. For example if I were baking a cake and needed to have one part sugar to four

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