1. Vocabulary from Quiz 1 Define: Whole Numbers: Whole numbers are the numbers beginning with zero and moving to the right. They do not include negative numbers. They are not fractions. Fractions : The comparison of a part to a whole.

2. Vocabulary Complex Fractions A fraction in which either the numerator, denominator, or both contain fractions. Improper Fractions A fraction in which the numerator is greater than the denominator. Mixed Numbers A mixed number is a whole number and a fraction expressed together.

3. Solve Study the next page to solve 4 3 /8 = Convert 16/4 to a whole number Convert 7 ½ to an improper fraction Convert 32/5 to a mixed number Divide 6/8 2/5

4. Traditional approach 4 bags of soil divided by 3/8 or the amount needed to complete one garden. Step 1: 4 3/8 = Step 2 4 X 8/3 = 32/3 Step 3 divide 3 into 32 = 9 5/3 gardens.

5. Improper Fraction A fraction in which the numerator is greater than the denominator. 16 4 Hint: 16/4 is equal to 4 wholes. The different ways to express fractions are representing the same amounts in different forms.

6. Jill ordered 3 bags of soil for her raised flower gardens. Each garden needs two thirds (2/3) of a bag of soil. How many gardens can she fill completely with soil? Directions: Build a model Build a ratio table Use the standard algorithm (invert and multiply) Does the algorithm give the answer in terms of soil or gardens?

7. Story problem Jill ordered 3 bags of soil for her raised flower gardens. Each garden needs 2/3 of a bag of soil. How many gardens can she fill completely with soil? ½ of a bag of garden 2/3 of a bag of soil

8. Questions How do we divide by soil and end up answering in gardens using the traditional approach? When we invert the fraction we are talking in terms of gardens instead of in terms of soil. Why do we invert and multiply in the standard algorithm? We invert and multiply so that we can get an answer in terms of what we want to know. It is related to the above question.

9. To get you started Ratio Table Garden 1 Soil 2/3

10. Practice Problems continued Solve using the traditional method 5 6/8 = 2 7/3 = 8 6/8 = 7 3/6 = 14 2/3 1 6/3 =

11. Vocabulary from Quiz 2 Define Coordinate Plane: a plane formed by the intersection of a horizontal number line with a vertical number line. Ratio : The comparison of one quantity to another. 3 lemons:4 apples The horizontal axis is the X axis. The vertical axis is the Y axis. Please put the x coordinate which is 3 and the y coordinate which is 4 in parentheses (3, 4 )

12. Pizza Party You decide to have a Pizza Party to celebrate the end of the trimester. You invite all of your friends and receive conformation that 60 of them will be attending your party. When you call the pizza joint they tell you that one large pizza with two toppings of your choice will cost $12.00 including tax. There are 15 pieces of pizza in each pizza. Each person eats an average of 5 pieces of pizza.

13. Directions What is the ratio of people to pieces of pizza? The ratio of people is 3:1. The reason is that if 3 people each eat 5 pieces of pizza then that totals one pizza. How many total pieces of pizza will you need to buy? If one pizza feeds 3 people and 60 people are coming than divide 60 by three which is 20. You need 20 pizzas and there are 15 slices in each pizza therefore 15 and 20 is 300 slices of pizza. How many total pizzas will you need to buy? If one pizza feeds 3 people and 60 people are coming than divide 60 by three which is 20 pizzas. How much is the total bill going to be? If one pizza costs $12.00 and you need 20 pizzas then 20 times 12 is $240 What is the cost per person? If 60 people are coming then take the total cost of $240.00 and divide that by 60. The cost per person is $4.00

14. Build a ratio table that shows pizza, person/people and, cost all the way from one person to 60 people. People 1 2 3 30 60 Cost $4.00 $8.00 $12.00 $120.00 $240.00 Pizzas 1/3 2/3 1 10 20 Slices 5 10 15 150 300

15. Build a Graph Using pizza has your x coordinate and people as your y coordinate construct a graph representing the line graph moving in only whole pizzas. Hint: Use your ratio table to find the information. Pizzas People

16. 0 1 10 20 Pizza The X and Y coordinates come right off of the ratio table to for a linear line graph. 60 30 3 0 People (20,60) (10,30) (1,3)