Unit 2. Day 1.

Today’s Lesson 1) What are rational numbers? 2) What are fractions 3) Simplifying fractions

What is a rational number?

What is a ratio? ratio : (comparison) the relationship that exists between the size, number, or amount of two things and that is often represented by two numbers

A ratio is a comparison of two quantities by division 5 4 Ratio of boys to girls: 5 to 4 5:4 4 5 Ratio of girls to boys: 4 to 5 4:5

Ratio of cars to planes: 6 to 4 3:2 6:4 3 to 2 Example A: Write each ratio as a fraction in simplest form 3 2 6 4 Ratio of cars to planes: 6 to 4 3:2 6:4 3 to 2 2 3 4 6 Ratio of planes to cars: 2 to 3 4 to 6 4:6 2:3

What is a ratio? ratio : FRACTION

Today’s Lesson 1) What are rational numbers? 2) What are fractions 3) Simplifying fractions

What are fractions?

What are fractions? 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 3 12 1 4 = =

What are fractions? 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 2 12 1 6 = =

What are fractions? 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 6 12 1 2 = =

What are fractions? 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 4 12 1 3 = =

What are fractions? 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 7 12 7 12 = =

What are fractions? 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 15 12 1 3 12 1 1 4 = = =

Today’s Lesson 1) What are rational numbers? 2) What are fractions 3) Simplifying fractions

Simplifying Fractions 6 12  1 2

Commercial Break 6 6 1 1 56 56 1 1 → → 8 8 1 1 324 324 1 1 → →

Example A: Write 18 24 in simplest form. ÷2 9 12 ÷3 3 4 ÷2 ÷3 Elementary School

Example A: Write 18 24 in simplest form. Middle School 3 18 24 1 2 ∙3∙ 3 1 = = 1 2 ∙2∙2∙ 1 4 3 24 18 4 6 3 6 2 3 2 2 2 3

Example A: Write 18 24 in simplest form. Middle School 18 24 3 4 2∙3∙3 = = 2∙2∙2∙3 24 18 4 6 3 6 2 3 2 2 2 3

Middle School Elementary School 3 4 18 24 = = 18 24 9 12 3 4 2∙3∙3 2∙2∙2∙3 18 24 ÷2 9 12 ÷3 3 4 ÷2 ÷3 Elementary School

Example B: Write 12 32 in simplest form. ∙ ∙3 1 2 3 = = 1 2 ∙ ∙2∙2∙2 1 2 8 32 4 8 12 2 2 2 4 3 4 2 2 2 2

Example B: Write 12 32 in simplest form. 3 8 2∙2∙3 = = 2∙2∙2∙2∙2 32 4 8 12 2 2 2 4 3 4 2 2 2 2

Example C: Write 20 75 in simplest form. Example D: Write 18 90 in simplest form.

Example C: Write 20 75 in simplest form. 4 15 2∙2∙5 = = 3∙5∙5 20 75 2 10 3 25 2 5 5 5

Example D: Write 18 90 in simplest form. 2∙3∙3 = = ? 2∙3∙3∙5 18 90 2 9 9 10 3 3 3 3 2 5

Example D: Write 18 90 in simplest form. ∙ ∙ 2 1 1 3 3 1 = = 1 2 ∙ ∙ ∙5 1 3 1 3 5 18 90 2 9 9 10 3 3 3 3 2 5

Example E: Write 70 42 in simplest form. 5 3 2∙5∙7 1 2 3 = = = 2∙3∙7 70 42 7 10 6 7 2 5 2 3

Example F*: Write 90 35 in simplest form. 18 7 2 4 7 2∙3∙3∙5 = = = 5∙7 90 35 9 10 5 7 3 3 2 5

Example G: Four inches is what part of one foot? 4 12 1 3 2∙2 = = 2∙2∙3 12 4 4 3 2 2 2 2

Example H: Mr. Jordan did a survey of the 260 RMS 7th graders Example H: Mr. Jordan did a survey of the 260 RMS 7th graders. He wanted to know what they liked better, Coke or Pepsi. 195 of the students prefer coke. Express the fraction in simplest form. 195 260 3 4 3∙5∙13 = = 2∙2∙5∙13 195 260 5 39 10 26 3 13 2 13 2 5