Comparing and Ordering Rational Numbers TeacherTwins©2014

Warm Up Identify all sets to which each number belongs. 1). 𝟕 𝟖 2) Warm Up Identify all sets to which each number belongs. 1). 𝟕 𝟖 2). -45 3). 3.76 4). 𝟐𝟖 𝟏𝟒 5). Simplify the following fraction: 𝟑𝟓 𝟏𝟎𝟎 Rational number Rational number, integer Rational number Rational number, integer, whole number 𝟕 𝟐𝟎

Comparing and Ordering Rational Numbers Flippable Comparing and Ordering Rational Numbers Comparing Fractions Comparing Decimals

Comparing and Ordering Fractions Method 1 Find the common denominator and compare the numerators. Which number is the smallest 𝟑 𝟒 or 𝟗 𝟏𝟎 ? 𝟑 𝟒 = 𝟏𝟓 𝟐𝟎 𝟗 𝟏𝟎 = 𝟏𝟖 𝟐𝟎 𝟏𝟓 𝟐𝟎 < 𝟏𝟖 𝟐𝟎 𝟑 𝟒 < 𝟗 𝟏𝟎

𝟑 𝟒 𝟗 𝟏𝟎 𝟑 𝟒 < 𝟗 𝟏𝟎 𝟐 𝟑 = 𝟒 𝟔 Method 2 𝟐 𝟑 𝟒 𝟔 Cross Multiply Example 1: 𝟑 𝟒 𝟗 𝟏𝟎 Example 2: 𝟐 𝟑 𝟒 𝟔 This number is larger so 9/10 is larger. 30 36 𝟑 𝟒 < 𝟗 𝟏𝟎 Both products are the same so they are equal. 𝟐 𝟑 = 𝟒 𝟔 12 12

Order from least to greatest. 7). 𝟏 𝟐 , 𝟐 𝟑 , 𝟓 𝟔 8). 𝟑 𝟖 , 𝟑 𝟒 , 𝟐 𝟑 Practice Replace with >, <, or =. 1). 𝟓 𝟏𝟐 ____ 𝟕 𝟏𝟐 2). 𝟓 𝟔 _____ 𝟕 𝟏𝟎 3). 𝟓 𝟔 ___ 𝟑 𝟓 4). 𝟐 𝟑 ____ 𝟓 𝟖 5). 𝟏 𝟑 ____ 𝟏𝟐 𝟑𝟔 6). 𝟒 𝟓 ____ 𝟐 𝟑 Order from least to greatest. 7). 𝟏 𝟐 , 𝟐 𝟑 , 𝟓 𝟔 8). 𝟑 𝟖 , 𝟑 𝟒 , 𝟐 𝟑 < > > > = > ½, 2/3, 5/6 3/8, 2/3, 3/4

Comparing and Ordering Decimals To compare decimals, line up the decimal points and compare the digits from left to right until you find different digits. Example: 0.726 ___ 0.724 the first digit that is different is 6 and 4 6>4 > Practice Use < , > or = to compare. 1). -0.245 _____ 0.124 2). 3.4567 ____ 3.45679 3). -4.56 _____ - 4.57 4). 0.98 ____ 0.980 < < > =

Closure Determine whether the following statement is true or false. Explain your reasoning. A rational number is always an integer. False, 𝟑 𝟓 is not a rational number.