1. A ratio is a comparison of one quantity to another.
6.RP Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
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

2. 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?

3. 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?
Oil
20%
Gas
20%
Gas
20%
Gas
20%
Gas
20%
Oil
25%
Gas
25%
Gas
25%
Gas
25%

4. What does each decimal or percentage mean in relation to the context?
Extension
Little Red Riding Hood has a basket that holds eight eggs. 5 of them are brown and 3 are white.
What are all the ratios of eggs? Hint: Think about comparing all sets, brown, white and totals.
Change all the ratios to fractions, decimals and percentages using a table.
What does each decimal or percentage mean in relation to the context?

5. 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?

6. Check for Understanding
Ratio
Decimal
Fraction
Percentage
White to Brown Eggs