Core Focus on Ratios, Rates and Statistics Lesson 1.1 Core Focus on Ratios, Rates and Statistics Ratios

Warm-Up Simplify each fraction. Write your answer as a proper or improper fraction, not as a mixed number.

Simplify and write ratios three ways. Lesson 1.1 Ratios Simplify and write ratios three ways.

Explore! Comparing Students Step 1 Write a fraction comparing the number of boys to the number of girls for each teacher . Write the fraction in simplest form. This fraction means for every ____ boys there are ____ girls. Step 2 Find the total number of students in each teacher’s class. Write a fraction comparing the number of boys to the total number of students for each teacher . Write the fraction in simplest form. This fraction means for every ____ boys there are ____ students. Step 3 Write a fraction comparing the number of girls to the total number of students for each teacher . Write the fraction in simplest form. This fraction means for every ____ girls there are ____ students.

Explore! Comparing Students Step 4 Count the number of boys and girls in your class. a. Find the fraction of boys to girls. This is the ratio of boys to girls. b. Find the ratio of boys to total number of students. c. Find the ratio of girls to total number of students. Step 5 Mr. Jansen’s math class has 3 boys for every 2 girls. a. Write a ratio of boys to girls in Mr. Jansen’s class. b. There are 30 students in Mr. Jansen’s class. How many are boys? Explain how you know your answer is correct.

Vocabulary Ratio A comparison of two numbers using division. Good to Know!  A ratio shows a part to another part or a part to a whole.  A ratio written as a fraction should be written in simplest form.  Ratios can be larger than 1.  Ratios larger than 1 should be written as simplified improper fractions.

Writing Ratios A ratio comparing two numbers, 3 and 5, can be written in three ways:  As a fraction →  Using a colon → 3 : 5  Using the word “to” → 3 to 5

Example 1 Paul took a handful of jelly beans. He chose 4 blue, 2 green, 3 red and 3 yellow. Write a ratio using each of the three ways. a. Compare blue jelly beans to red jelly beans. Fraction Using a Colon Using “to” a. 4 : 3 4 to 3

Example 1 Continued… Paul took a handful of jelly beans. He chose 4 blue, 2 green, 3 red and 3 yellow. Write a ratio using each of the three ways. b. Compare green jelly beans to the total number of jelly beans. Fraction Using a Colon Using “to” b. Total number of jelly beans: 4 + 2 + 3 + 3 = 12 1 : 6 1 to 6

Example 1 Continued… Paul took a handful of jelly beans. He chose 4 blue, 2 green, 3 red and 3 yellow. Write a ratio using each of the three ways. c. Compare red jelly beans to the total number of jelly beans. Fraction Using a Colon Using “to” b. Total number of jelly beans: 4 + 2 + 3 + 3 = 12 1 : 4 1 to 4

Example 2 The ratio of boys to girls on a soccer team is 8 : 7. What is the ratio of boys to all players on the soccer team? The ratio 8 : 7 means there are 8 boys for every 7 girls. For every 8 boys there are 15 (8 + 7) players. This makes the ratio of boys to all players 8 : 15.

Example 3 Compare the number of stars to the number of circles. If the ratio remains the same, how many stars will you have if you have 14 circles? Write the ratio of stars to circles as a fraction. Simplify the ratio. Find an equivalent ratio that has 14 circles. You will have 35 stars. The ratio 35 : 14 is equivalent to 10 : 4. The amount of stars and circles changed, but the ratio of stars to circles did not change.

Example 4 Petra is filling jars with marbles. The jar sizes change, but the ratio of blue marbles to green marbles always stays the same. The table below shows some of the jars and their quantity of blue marbles to green marbles. a. Find the ratio of blue marbles to green marbles in each jar. Choose any pair of blue and green values and write the ratio as a fraction. Simplify the ratio. The ratio of blue marbles to green marbles is 3 : 5 or . blue 6 12 18 27 33 green 10 20 30 45 ? The different quantities used to make a ratio can also be written in a table and the points graphed.

Example 4 Continued… Petra is filling jars with marbles. The jar sizes change, but the ratio of blue marbles to green marbles always stays the same. The table below shows some of the jars and their quantity of blue marbles to green marbles. b. Find the number of green marbles when the jar has 33 blue marbles. Find an equivalent ratio to that has 33 blue marbles. There would be 55 green marbles when the jar has 33 blue marbles. blue 6 12 18 27 33 green 10 20 30 45 ?

Example 4 Continued… Petra is filling jars with marbles. The jar sizes change, but the ratio of blue marbles to green marbles always stays the same. The table below shows some of the jars and their quantity of blue marbles to green marbles. c. Let the number of blue marbles be x and the number of green marbles be y. Plot the ordered pairs (x, y) for each set of values in the table. What do you notice about the points? Graph each of the ordered pairs (6, 10), (12, 20), (18, 30), (27, 45) and (33, 55). The points are all in a line with the origin (0, 0). Each point has a ratio of its y-value to its x-value of . blue 6 12 18 27 33 green 10 20 30 45 ? Number of Marbles in Jars

Communication Prompt The ratio of boys to girls in math class is 1 : 2. What does this ratio mean?

Exit Problems Simplify the ratio 100 : 20 and write the ratio as a fraction, with a colon and using the word “to”.   Lucas had 6 red jelly beans and 9 purple jelly beans. Write each ratio as a fraction in simplest form. Write the ratio of the number of red jelly beans to the number of purple jelly beans. Write the ratio of the number of red jelly beans to the total number of jelly beans Lucas has.