Transcript Document

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.
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
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.
Oil
20%
Gas
20%
Gas
20%
Gas
20%
Gas
20%
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
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
Ratio
Flour
Water
Decimal
Percent
Fraction
Application
Protein Shake
Mix Plain
Amount
Protein
Calories
Milk Powder
3tbsp
4.44 g
44.7
Soy Protein
Isolate
2 tbsp.
8g
36
Whey protein
Isolate 90%
2 tbsp.
8.8
36
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 Plain
Amount
Protein
Calories
Milk Powder
3tbsp
4.44 g
44.7
Soy Protein Isolate
2 tbsp.
8g
36
Whey protein Isolate 90%
2 tbsp.
8.8
36
Directions
Mix in 8 oz. water
• Challenge
• How would the ratio table look for protein and
calories?
Protein Shake Mix Plain
Amount
Protein
Calories
Milk Powder
3tbsp
4.44 g
44.7
Soy Protein Isolate
2 tbsp.
8g
36
Whey protein Isolate 90%
2 tbsp.
8.8
36
Directions
Mix in 8 oz. water