Lesson 2 Compare and Order Rational Numbers Lesson

Lesson 2 Compare and Order Rational Numbers

Lesson 2: Compare and Order Rational Numbers Objective: SWBAT compare and order rational numbers. Do Now: Worksheet # 1 - 6

Lesson 2: Compare and Order Rational Numbers Definitions Rational Number is a number that can be expressed as a ratio of two integers. Common denominator is a common multiple of the denominators of two or more fractions. Least Common Denominator is the least common multiple of the denominators.

Natural Numbers – 1, 2, 3, 4, ……. . Whole Numbers – 0, 1, 2, 3, 4, ……. . Integers - ……-4, -3, -2, -1, 0, 1, 2, 3, 4, ……. . Rational Numbers – any number that can be written as a ratio, a/b Irrational Numbers – any number that is not a rational number ≠ a/b Real Numbers – all the rational and irrational numbers

Lesson 2: Compare and Order Rational Numbers Write the numbers from the list in the proper section of the Venn Diagram. 0. 8 ∏ . 2222…… -1/2 -1 20% 5 1 2 3

Lesson 2: Compare and Order Rational Numbers To compare rational numbers use symbols: • < (less than) • > (greater than) • = (equal) You can compare rational numbers in decimal or fraction form. When comparing rational numbers in decimal form: • Compare by place value (left to right) 0. 12 < 0. 25 0. 45 > 0. 4 -2. 33 < -1. 2 -

Lesson 2: Compare and Order Rational Numbers When comparing rational numbers a number line can be helpful. • Graph the numbers on a number line • The number to the left is less than the number to the right (use the < symbol) • The number to the right is greater than the number to the left (use the > symbol) Compare -1 -2 ____ -1 -1 0 1 2

Lesson 2: Compare and Order Rational Numbers You can also compare numerators. -1 ____ -1 - ____ - 11 < -7 -1 < -1 change to improper fraction compare numerators

Lesson 2: Compare and Order Rational Numbers When comparing rational numbers with different denominators. • Find the LCD (least common denominator) • Change each fraction to equivalent fractions using the LCD • Compare the numerators Compare LCD is 36 ____ X X 3 3 X X > 2 2 then >

Lesson 2: Compare and Order Rational Numbers ** You can find a common denominator just by multiplying the two denominators How to find the LCD 1. List multiples of the largest denominator and see if the other denominator is a factor Example: 1 2 10 8 10 is the larger 10: 10, 20, 30, 40 LCD is 40 8 is a factor of 40 Try It! 12 and 30

Lesson 2: Compare and Order Rational Numbers 2. - Find the GCF and divide it into either number - Multiply the quotient to the other number Example: 1 2 10 8 2 is the GCF 10/2 = 5 LCD is 40 5 x 8 = 40 Try It! 12 and 30

Lesson 2: Compare and Order Rational Numbers 3. - Find a factor of both numbers until the only factor is 1 - Multiply all factors to remaining numbers Example: 1 2 10 8 1 5 4 2 x 1 x 5 x 4 = 40 Try It! 12 and 30

Lesson 2: Compare and Order Rational Numbers 4. Use Prime Factorization method 1 2 10 8 10 2 x 5 8 2 x 4 2 x 2 LCD: 2 x 2 x 5 = 40 Try It! 12 and 30 multiply the most of each prime number

Lesson 2: Compare and Order Rational Numbers Try It! a. 4 7 5 8 b. -3 2 3 c. -5 7 -3 4 6 -2 7

Lesson 2: Compare and Order Rational Numbers When ordering rational numbers: • change number to decimal • line up by decimal point and compare by place value Order the set {3. 44, 3. 44000 3. 14159… 3. 14000 3. 44444… Answer: 3. 14, , 3. 14, 3 rd 2 nd 1 st 4 th , 3. 44, } least to greatest

Lesson 2: Compare and Order Rational Numbers Try It! a. {23%, 0. 21, , } b. {7. 49, , 7. 5%} c. {-1. 4, -1. 25}

Classwork • Guided Practice #1 -5 • Independent Practice #1 -10 • Problem Solving Practice #1 - 8

Closure Question: What is the easiest way to compare rational numbers? Exit Ticket Homework: Practice # 1 -25

Exit Ticket Compare <, >, or =. 1. 3 5 8 6 2. . 2 20% Order least to greatest. 3. {0. 43, 4%, . 4, 4. 1}

Homework