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Objective: Compare and order Rational numbers

Least Common Denominator Vocabulary: Rational Numbers Irrational Number Common Denominator Least Common Denominator

What is a rational number??? any number that can be expressed as a fraction Ex. Fractions, decimals, %’s, and integers (whole #’s that are + and -)

Examples of Rational Numbers -5 -1.444… 20% Integers 0.8 -3 5 -27 1 2 -35 Whole Numbers 6 2.22 1 3 35 1.3

a number that does not terminate AND does not repeat Irrational Number: a number that does not terminate AND does not repeat

Pi (π) is an irrational number… 3.1415926535897932384626433832795028841971693993751 05820974944592307816406286208998628034825342117067 98214808651328230664709384460955058223172535940812 84811174502841027019385211055596446229489549303819 64428810975665933446128475648233786783165271201909 14564856692346034861045432664821339360726024914127 37245870066063155881748815209209628292540917153643 67892590360011330530548820466521384146951941511609 43305727036575959195309218611738193261179310511854 80744623799627495673518857527248912279381830119491

A common number that both denominators fit into Common Denominator: A common number that both denominators fit into Examples

Comparing Rational Numbers Which is greater, or ? 7 9 2 9 When two fractions have the same denominator, just compare the numerators. 7 9 2 9 > because 7 > 2.

the smallest number that both denominators will fit into. Least Common Denominator (LCD): the smallest number that both denominators will fit into. Examples

Which is greater, or ? 3 4 4 5 When two fractions have different denominators, find the LCD, then compare.

Which is greater, or ? What’s the LCD of both fractions? 3 4 4 5 The LCD of the denominators 4 and 5 is 20. Answer:

Compare the Following Fractions < > <

Additional Example 1A: Comparing Fractions Course 2 2-11 Comparing and Ordering Rational Numbers Additional Example 1A: Comparing Fractions Compare the fractions. Write < or >. 7 9 5 8 The LCM of the denominators 9 and 8 is 72. 7 9 7 · 8 9 · 8 56 72 = Write equivalent fractions with 72 as the denominator. = 5 8 5 · 9 8 · 9 45 72 = = Compare the numbers. 56 72 > 45 , and so . 7 9 > 5 8

Ordering Rational Numbers To put decimals in order, line up the decimal points and compare using place value.

Ordering Rational Numbers Compare the decimals > 0.427 0.425 0.427 Compare the numbers that are different… 7 > 5 so… 0.42 5

Additional Example 3: Ordering Fractions and Decimals Course 2 2-11 Comparing and Ordering Rational Numbers Additional Example 3: Ordering Fractions and Decimals 4 5 Order , 0.93, and 0.9 from least to greatest. Write as decimals with the same number of places. 4 5 = 0.80 0.93 = 0.93 0.9 = 0.90 Graph the numbers on a number line. 0.93 0 0.2 0.4 0.6 0.8 1 0.80 < 0.90 < 0.93 Compare the decimals in order. 4 5 From least to greatest, the numbers are 0.9, 0.93, .

Insert Lesson Title Here Course 2 2-11 Comparing and Ordering Rational Numbers Insert Lesson Title Here Lesson Practice Compare the fractions. Write > or <. 1. Compare the decimals. Write < or >. 3. 0.32 and 0.312 3 7 4 10 5 8 2 3 or > 2. < or > 5 6 4. Order , 0.8, 0.826 from least to greatest. 0.8, 0.826, 5 6

Converting Fractions to Decimals To convert a Fraction to a Decimal manually, follow these steps: Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s. Step 2: Multiply both top and bottom by that number. Step 3. Then write down just the top number, putting the decimal place in the correct spot (one space from the right for every zero in the bottom number)

Method #1: Converting with Proportions Example # 1: Express 3/4 as a Decimal Step 1: We can multiply 4 by 25 to become 100 Step 2: Multiply top and bottom by 25 3 = 75 4 100

Example # 1 continued…. Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros); Answer = 0.75 Can you explain what we just did? Try to express ¼ as a decimal using method # 1.

Try to express ¼ as a decimal using method # 1.

Method #2: Convert by Dividing Example #1: to write 5/8 as a decimal, we need to calculate 5 ÷ 8: 0.625 8 √ 5.000 So = 0.625 as a decimal. Try this example: write 4/5 as a decimal using division (method #2).

write 4/5 as a decimal using division (method #2)

Write 3/8 as a decimal using division (method 2)

Write 2/7 as a decimal using division (method 2)

Convert decimals to Percents To convert a decimal to a percent Step 1:Multiply the decimal Step 2: Move the decimal by 100. to the right two places. 0.45

Convert decimals to Percents 0.38 0.235 0.005 1.05 0.023