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. The expression a < b means a is the left of b on the number line. b a a b

Using the Number Line The expression -1 > -3 means -1 is to the right of -3 on the number line. The expression -3 < -1 means -3 is the left of -1 on the number line

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 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 3: Which symbol makes this sentence true? Use >, <, or = Step 1: Align the numbers on the decimal point. Compare the whole numbers first. 15 = 15 Step 2: Compare the tenths place..3 =.3 Step 3: Compare the hundredths place.._9 >._6 Stop when one place value is larger than the other

Comparing Rational Numbers 1, 1.5, -1.5,.5

Converting Fractions into Decimals

Converting Fractions into Decimals

Converting Mixed Numbers into Decimals 2-3.2

Review

Fractions & Mixed Numbers on the Number Line

Remember when... You created boxes to represent fractions? 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? 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! Where you stop is where the fraction is on the number line!

Let’s Try It Again! Where you stop is where the fraction is on the number line!

Remember…Remember… ALWAYS start shading at zero!

What About Negative Fractions? Where you stop is where the fraction is on the number line!

Remember…Remember… ALWAYS start shading at zero!

Let’s Try Another Negative Fraction! Where you stop is where the fraction is on the number line!

Let’s Take It to the Next Level! Where you stop is where the fraction is on the number line!

Let’s Try It Again! Where you stop is where the fraction is on the number line!

Remember…Remember… ALWAYS start shading at zero!

What About Mixed Numbers? Where you stop is where the fraction is on the number line!

Remember…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 many spaces are in the box for the denominator. Then starting at 0, shade each space until you reach the letter for the numerator. However many spaces you shade is the numerator!

Remember…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 many spaces are in the box for the denominator. Then starting at 0, shade each space until you reach the letter for the numerator. However many spaces you shaded is the numerator!

Remember…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 many spaces are in the box for the denominator. Then starting at 0, shade each space until you reach the letter for the numerator. However many spaces you shade is the numerator!

Remember…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 many spaces are in the box for the denominator. Then starting at 0, shade each space until you reach the letter for the numerator. However many spaces you shaded is the numerator!