Transcript Comparing and Ordering Rational Numbers

Comparing and
Ordering Rational
Numbers
Coach Lesson 5
Also see textbook pages 108 - 110
Jeff Rhodus
6th Grade
Elsanor Elementary
Getting the Idea!
Sometimes, you need to order numbers that are in
different forms.
For example, you may need to order a set of numbers
that includes whole numbers and decimals.
A good strategy to use to order whole numbers and
decimals is to first compare the whole-number parts of
all the numbers. Then compare the decimal parts if
necessary.
Example: 10 > 9.25 > 8.1 because 10 > 9 > 8
You can use the same strategy to order whole numbers
and mixed numbers.
First, compare the whole number parts.
Then compare the fractional parts if necessary.
Example: 5 > 4 21 > 312 because 5 > 4 > 3
Example 1: Order these numbers from least to greatest.
3
4
2
1.5
Strategy: Compare the whole-number parts. Then
compare the fractional parts if needed.
Compare the whole-number parts first.
2 is a whole number.
3/4 is the same as 0
3
+4
,so its whole number part is 0.
1.5 has 1 as its whole-number part
0 < 1 < 2, so
3
4
< 1.5 < 2
Solution: The numbers in order from least to greatest are: 3 ,
4
1.5, 2
Example 2: Order these numbers from greatest to least.
3
2 56
2
1
4
Strategy: Compare the whole number parts. Then compare the
fractional parts.
Step 1: Compare the whole number parts first.
3 > 2 so 3 is greater than both 2
5
6
and 2
1
4
2 65 and 2 14 each have the same whole number part, 2,
so compare the fractional parts.
Step 2: Compare the fractional parts of the remaining
numbers.
Just look at the fractional parts: 5/6 and 1/4
The least number that is a multiple of both 6 and 4 is 12.
Rewrite each fraction as an equivalent fraction with a
denominator of 12.
5
6
= 65 xx 22 = 10
12
10
12
1
4
3
>12
so
5
6
3
= 14 xx 33 = 12
>
1
4
Solution: The numbers in order from greatest to least
is: 3, 2 2 56 1
4
Sometimes ordering numbers requires you to compare
fractions, decimals, and percents. A good strategy for
doing this is to put all the numbers into the same form.
That means converting all numbers to fractions or
converting all numbers to decimals.
Coached Example: Order these numbers from
greatest to least.
72%
7
110
1.78
7
25
Thinking it Through:
Convert all the numbers to decimals with two places after the _______.
72%= ______
1
= ______
1.78 = ______
7/25 = ______
Order the decimals from greatest to least: _____ > _____ > _____ > _____
The numbers ordered from greatest to least are: _____, _____, _____, _____