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 7.ns.3 Solve real- world and mathematical problems involving the four operations with rational numbers. 7.NS.2 Apply and extend previous understanding of multiplication and division of fractions t o multiply and divide rational numbers.

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?

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%

Application Questions You have a solution of water and flour mix. The ratio is 1 part water to 3 parts flour. What is the fraction as expressed in terms of water? In terms of flour.

Applying forward The fraction of the mixture is ¼ in terms of water or ¾ in terms of water. If you wanted to dilute the fraction by half what would you do? What would the problem look like? Think Pair Share Convert your answer into a percentage and decimal both in terms of water and in terms of flour.

Continued ¼ / ½ = (Expressed in terms of water) ¾ / ½ ( Expressed in terms of flour) Build a table showing the answer in percentages, decimals, ratios and fractions in terms of flour and water.

Continued RatioDecimalPercentFraction Flour Water

Application Protein Shake Mix Plain AmountProteinCalories Milk Powder3tbsp4.44 g44.7 Soy Protein Isolate 2 tbsp.8g36 Whey protein Isolate 90% 2 tbsp Directions Mix in 8 oz. water

Application Considering only the far left column regarding milk powder, soy protein and whey isolate how could you use ratios to calculate the amounts needed in 36 ounces of water? Think Pair Share

Continued Second Question You have 3 gallons of milk powder stored in your pantry. Use ratios to solve how much whey isolate and soy isolate you would need to use the entire 3 gallons of milk powder. What if you only had 1 ½ gallons of milk powder. Use ratios to solve how much whey isolate and soy isolate you would need to use the entire 1 ½ gallons of milk.

Draw a Ratio Table using the recipe to show what you would need if you made a ½, ¼ and ten times the amount of the batch represented. Protein Shake Mix PlainAmountProteinCalories Milk Powder3tbsp4.44 g44.7 Soy Protein Isolate2 tbsp.8g36 Whey protein Isolate 90%2 tbsp Directions Mix in 8 oz. water

Challenge How would the ratio table look for protein and calories? Protein Shake Mix PlainAmountProteinCalories Milk Powder3tbsp4.44 g44.7 Soy Protein Isolate2 tbsp.8g36 Whey protein Isolate 90%2 tbsp Directions Mix in 8 oz. water