Unit 2. Day 1.

Go Over Test

Your Grade

Unit 2: Rational Numbers Unit 1: Integers

Please get out paper for today’s lesson Name Date Period -------------------------------------------------------- Topic: Rational Numbers… What they are & how to simplify them “Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.”

Today’s Lesson 1) What are rational numbers? 2) Simplifying fractions (6th grade) 3) Simplifying fractions (7th grade)

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

What is a ratio? ratio : FRACTION

Today’s Lesson 1) What are rational numbers? 2) Simplifying fractions (6th grade) 3) Simplifying fractions (7th grade)

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 E: Write 70 42 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

Today’s Lesson 1) What are rational numbers? 2) Simplifying fractions (6th grade) 3) Simplifying fractions (7th grade)

𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑠 − 𝑝 𝑞 −𝑝 𝑞 𝑝 −𝑞 = =

𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑠 − 1 2 −1 2 1 −2 −1 −2 = = =

𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑠 2 3 −

Example F: Write − 18 24 in simplest form. −18 − 18 24 3 4 2∙3∙3 − = = −1 18 2∙2∙2∙3 2 9 18 24 −3 −1∙2∙3∙3 3 3 = = − 2∙2∙2∙3 4 24 18 4 6 3 6 2 3 2 2 2 3

Example G*: Write − 90 225 in simplest form. Example H*: Write −12 210 in simplest form. Example I*: Write 56 −52 in simplest form.

Example G*: Write − 90 225 in simplest form. −90 −1 90 − 90 225 2 5 2∙3∙3∙5 − = = 3∙3∙5∙5 9 10 2 5 3 3 90 225 −2 −1∙2∙3∙3∙5 225 = − = 3∙3∙5∙5 5 4 5 90 5 45 5 2 2 5 5 − 2 0 9 10 5 9 2 − 25 3 3 2 5 3 3

Example H*: Write −12 210 in simplest form. −12 210 1 −1∙ ∙2∙ 2 1 3 −2 = = ∙ ∙5∙7 2 1 1 3 3 4 35 2 2 − 12 210 2 35 2∙2∙3 = = − 2∙3∙5∙7 −12 210 −1 12 21 10 2 6 3 7 2 5 2 3

Example I*: Write 56 −52 in simplest form. 2∙ ∙ ∙7 2 1 2 1 14 = = 2 26 −1∙ ∙ ∙13 2 1 1 2 −13 2 13 56 52 14 13 2∙2∙2∙7 − = = 2∙2∙13 − 56 −52 2 6 8 −1 2 5 2 2 7 52 − 4 2 4 2 26 1 − 1 2 2 2 2 13

Homework 2.1 #1-15