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Comparing & Ordering Rational Numbers MCC6.NS.7.a MCC6.NS.7.b MCC6.NS.7.d Comparing Rational Numbers To compare rational numbers, we use the symbols: > (greater than) < (less than) = (equal to) > (greater than or equal to) < (less than or equal to) Using the Number Line The expression a > b means a is to the right of b on the number line. b a The expression a < b means a is the left of b on the number line. a b Using the Number Line The expression -1 > -3 means -1 is to the right of -3 on the number line. -3 -1 The expression -3 < -1 means -3 is the left of -1 on the number line. -3 -1 Common Misconception with Comparing Numbers Some students think the greatest number is the number closest to zero. NOPE! Because that rule is not always true. -5 -2 0 10 -2 is closer to 0 than -5 and is greater than -5… but -2 is closer to 0 than 10 but is less than 10. Example 1: Order the following numbers from greatest to least. Use the number line to justify the order. 7, -3, 5, -5, 10, -10, 4, 0 Example 2: Which symbol makes this sentence true? Use >, <, or = Step 1: Step 2: Step 3: Step 4: 3½ 3¼ Compare the whole-number parts. 3=3 Find a common denominator for the fraction parts. 2: 2, 4, 6 4: 4, 8, 12 Rewrite the fractions with a common denominator. 𝟏 𝟐 = 𝟐 𝟒 Compare the fractions. 𝟐 𝟏 > 𝟒 𝟒 Example 3: Which symbol makes this sentence true? Use >, <, or = 15.36 15.391 Step 1: Align the numbers on the decimal point. Compare the whole numbers first. 15 = 15 15.36 Step 2: Compare the tenths place. 15.391 .3 = .3 Step 3: Compare the hundredths place. ._9 > ._6 Stop when one place value is larger than the other. Comparing Rational Numbers Rational numbers are written in different forms. 1. Change them into the same form. 2. Use the number line to help compare the numbers. 1.5, 𝟏 1 , 𝟐 -.5, 50% 1, 1.5, -1.5, .5 -2 -1 0 1 2 Converting Fractions into Decimals To convert a fraction into a decimal, divide the numerator by the denominator. 1 2 0.5 2| 1.0 -10 0 Converting Fractions into Decimals Let’s practice! 3 4 1 5 Converting Mixed Numbers into Decimals Temporarily ignore the whole number. Convert the fraction into a decimal. Place the whole number in front of the decimal. 3 2 4 2 1 -3 5 -3.2 Review A. 1 4 .25 B. 2 5 .4 C. 1 2 8 2.125 D. 1 − 2 -.5 Fractions & Mixed Numbers on the Number Line Remember when... You created boxes to represent fractions? 1 3 First, you drew a rectangular box. Then you used the denominator to split the box. Then you used the numerator to shade the box. Do You Remember Now? 3 4 First, you drew a rectangular box. Then you used the denominator to split the box. Then you used the numerator to shade the box. Let’s Take It to the Next Level! 1 Place on the number line. 3 Do the same thing as before! Just put the box on the line! Where you stop is First, draw a box from 0 to 1. where the fraction is Then use the denominator to split the box. on the number line! Then use the numerator to shade the box. Let’s Try It Again! 3 Place on the number line. 4 Do the same thing as before! Just putyou thestop box on Where is the line! First,the draw a box from where fraction is 0 to 1. Then use the denominator to split the box. on the number line! Then use the numerator to shade the box. Remember… ALWAYS start shading at zero! What About Negative Fractions? 1 Place - on the number line. 3 Do the same thing as before! Just put the box on the line! Where youdraw stop is from 0 to -1. This time, a box where the is to split the box. Then use thefraction denominator on the line!to shade the box. Then usenumber the numerator Remember… ALWAYS start shading at zero! Let’s Try Another Negative Fraction! 3 Place − on the number line. 4 Do the same thing as before! Just put the box on the line!is Where you stop This time, where draw a box 0 to -1. is thefrom fraction Then use the denominator to split the box. on the number line! Then use the numerator to shade the box. Let’s Take It to the Next Level! 1 Place1 on the number line. 3 Start at the whole number on the number line. Put the box on the line between the whole numberWhere & the next youinteger. stop is First, draw a box from 1 to 2. wheretothe is Then use the denominator split fraction the box. Then use the numerator to shade the box.line! on the number Let’s Try It Again! 3 Place on the number line. 4 Do the same thing as before! Just putyou thestop box on Where is the line! First,the draw a box from where fraction is 0 to 1. Then use the denominator to split the box. on the number line! Then use the numerator to shade the box. Remember… ALWAYS start shading at zero! What About Mixed Numbers? 1 Place -3 on the number line. 3 Do the same thing as before! Just put the box on the line! Where youdraw stop is from -3 to -4. This time, a box where the is to split the box. Then use thefraction denominator on the line!to shade the box. Then usenumber the numerator Remember… ALWAYS start shading at zero! But… What If I Have to Name the Fraction? Name That Fraction! What rational number does A represent? Just use the lines that are there! Draw the box from 0 to 1. Count how manymany spaces are in the box for the However denominator. spaces you shade is Then starting at 0, shade each space until you reach the the numerator! letter for the numerator. Remember… ALWAYS start shading at zero! Name That Fraction! What rational number does A represent? Just use the lines that are there! Draw the box from 0 to 1. Count how manymany spaces are in the box for the However denominator. spaces you shaded Then starting at 0, shade each space until you reach the is the numerator! letter for the numerator. Remember… ALWAYS start shading at zero! Name That Negative Fraction! What rational number does A represent? Just use the lines that are there! Draw the box from 0 to -1. Count how manymany spaces are in the box for the However denominator. spaces you shade is Then starting at 0, shade each space until you reach the the numerator! letter for the numerator. Remember… ALWAYS start shading at zero! Try Again! What rational number does A represent? Just use the lines that are there! Draw the box from 0 to -1. Count how manymany spaces are in the box for the However denominator. spaces you shaded Then starting at 0, shade each space until you reach the is the numerator! letter for the numerator.