Core Focus onRatios, Rates and Statistics

Ratios

Lesson 1.1

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

1.

2.

3.

4.

15

10

36

48

7

14

40

16

23

25

2 or 2

1

43

Ratios

Simplify and write ratios three ways.

Lesson 1.1

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.

Step 5 Mr. Jansen’s math class has 3 boys for every 2 girls.

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.

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.

RatioA comparison of two numbers using division.

Vocabulary

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

5

3

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.

Example 1

Fraction Using aColon

Using“to”

a. 4 : 3 4 to 3blue jelly beans 4

red jelly beans 3

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 numberof jelly beans.

Example 1 Continued…

Fraction Using aColon

Using“to”

b. Total number of jelly beans:4 + 2 + 3 + 3 = 12

1 : 6 1 to 6

green jelly beans 2 1

total jelly beans 12 6

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 numberof jelly beans.

Example 1 Continued…

Fraction Using aColon

Using“to”

b. Total number of jelly beans:4 + 2 + 3 + 3 = 12

1 : 4 1 to 4

red jelly beans 3 1

total jelly beans 12 4

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 2

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.

Example 3

10 54 2

The amount of stars and circles changed, but the ratio of stars to circles

did not change.

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 valuesand write the ratio as a fraction.

Simplify the ratio.

The ratio of blue marbles to green marbles is 3 : 5 or .

Example 4

The different quantities used to make a ratio can also be written in a table and the points graphed.6 3

10 5

3

5

blue 6 12 18 27 33

green 10 20 30 45 ?

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.

Example 4 Continued…

3

5

blue 6 12 18 27 33

green 10 20 30 45 ?

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 theorigin (0, 0). Each point has a ratioof its y-value to its x-value of .

Example 4 Continued…

53

blue 6 12 18 27 33

green 10 20 30 45 ?

Number of Marbles in Jars

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

Communication Prompt

1. Simplify the ratio 100 : 20 and write the ratio as a fraction, with a colon and using the word “to”. 

2. Lucas had 6 red jelly beans and 9 purple jelly beans. Write each ratio as a fraction in simplest form.

a. Write the ratio of the number of red jelly beans to the number of purple jelly beans.

b. Write the ratio of the number of red jelly beans to the total number of jelly beans Lucas has.

Exit Problems

51; 5 : 1; 5 to 1

23

or 2 : 3

25

or 2 : 5