Comparing & Ordering Rational Numbers

MCC6.NS.7.a MCC6.NS.7.bMCC6.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.

-3 -1

-3 -1

Common Misconception with Comparing NumbersSome 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 =

3 ½ 3 ¼ Step 1: Compare the whole-number parts.

3 = 3Step 2: Find a common denominator for the

fraction parts.2: 2, 4, 6

4: 4, 8, 12 Step 3: Rewrite the fractions with a common

denominator.

Step 4: Compare the fractions.

>

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 = 15Step 2: Compare the tenths place.

.3 = .3Step 3: Compare the hundredths place.

._9 > ._6Stop when one place value is larger than the

other.

>

15.3615.391

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, -.5, 50%

-2 -1 0 1 2

1, 1.5, -1.5, .5

Converting Fractions into Decimals

To convert a fraction into a decimal, divide the numerator by the denominator.

0.5-10 0

Converting Fractions into Decimals

Let’s practice!

Converting Mixed Numbers into

DecimalsTemporarily ignore the whole number.Convert the fraction into a decimal.

Place the whole number in front of the decimal.

-3 2 -3.2

ReviewA.

B.

.25

.42.125-.5

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.

13

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.

34

Let’s Take It to the Next Level!Place on the number line.

Do the same thing as before!Just put the box on the line!

First, draw a box from 0 to 1.Then use the denominator to split the box.Then use the numerator to shade the box.

0 1Where you stop is where the fraction is on the number

line!

𝟏𝟑

Let’s Try It Again!Place on the number line.

Do the same thing as before!Just put the box on the line!

First, draw a box from 0 to 1.Then use the denominator to split the box.Then use the numerator to shade the box.

0 1𝟑𝟒Where you stop is

where the fraction is on the number

line!

Remember…

ALWAYS start shading at zero!

What About Negative Fractions?

Place - on the number line.

Do the same thing as before!Just put the box on the line!This time, draw a box from 0 to -1.

Then use the denominator to split the box.Then use the numerator to shade the box.

-1 0−𝟏𝟑

Where you stop is where the fraction is on the number

line!

Remember…

ALWAYS start shading at zero!

Let’s Try Another Negative Fraction!

Place on the number line.

Do the same thing as before!Just put the box on the line!This time, draw a box from 0 to -1.

Then use the denominator to split the box.Then use the numerator to shade the box.

-1 0−𝟑𝟒 Where you stop is

where the fraction is on the number

line!

Let’s Take It to the Next Level!Place1 on the number line.

Start at the whole number on the number line.

Put the box on the line between the whole number & the next integer.

First, draw a box from 1 to 2.Then use the denominator to split the box.Then use the numerator to shade the box.

1 2Where you stop is where the fraction is on the number

line!

𝟏𝟑

Let’s Try It Again!Place on the number line.

Do the same thing as before!Just put the box on the line!

First, draw a box from 0 to 1.Then use the denominator to split the box.Then use the numerator to shade the box.

0 1𝟏𝟑𝟒Where you stop is

where the fraction is on the number

line!

Remember…

ALWAYS start shading at zero!

What About Mixed Numbers?

Place -3 on the number line.

Do the same thing as before!Just put the box on the line!This time, draw a box from -3 to -4.

Then use the denominator to split the box.Then use the numerator to shade the box.

-4 -3−𝟑𝟏𝟑

Where you stop is where the fraction is on the number

line!

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!

𝑨

0 1

321 __

A =

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!

421 __

A =

𝑨

0 1

3

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!

𝑨

-1 0

123 -__

A = -

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!

4 2 1 -__

A = -

𝑨

-1 0

3