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, …… 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 ____ -1 -2 -1 1 2

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

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 3 X 2 X 3 X 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 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 8 is a factor of 40 LCD is 40 Try It! 12 and 30

Lesson 2: Compare and Order Rational Numbers - 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 5 x 8 = 40 LCD is 40 Try It! 12 and 30

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

Lesson 2: Compare and Order Rational Numbers Try It! 4 5 7 8 -3 2 -3 4 3 6 -5 - 2 7 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, , 3.14, } least to greatest 3.44000 3rd 3.14159… 2nd 3.14000 1st 3.44444… 4th Answer: 3.14, , 3.44,

Lesson 2: Compare and Order Rational Numbers Try It! {23%, 0.21, , } {7.49, , 7.5%} {-1.4, -1 , -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 =. 3 5 8 6 .2 20% 3 5 8 6 .2 20% Order least to greatest. 3. {0.43, 4%, .4, 4.1}

Homework