Comparing and Ordering Rational Numbers

1
Comparing and Ordering Rational Numbers

• Coach Lesson 5
• Also see textbook pages 108 - 110
• Jeff Rhodus
• 6th Grade
• Elsanor Elementary

2
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 gt 9.25 gt 8.1 because 10 gt 9 gt 8
3
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.
1
Example 5 gt 4 gt 3 because 5 gt 4 gt 3
1
2
2
4
Example 1 Order these numbers from least to
greatest.
3
2
1.5
4
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
3/4 is the same as 0 ,so its whole number
part is 0.
4
1.5 has 1 as its whole-number part
3
0 lt 1 lt 2, so lt 1.5 lt 2
4
3
, 1.5, 2
Solution The numbers in order from least to
greatest are
4
5
Example 2 Order these numbers from greatest to
least.
5
3 2 2
1
6
4
Strategy Compare the whole number parts. Then
compare the fractional parts.
Step 1 Compare the whole number parts first.
1
5
3 gt 2 so 3 is greater than both 2 and 2
6
4
5
1
2 and 2 each have the same whole number
part, 2, so compare the fractional parts.
6
4
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.
6
Rewrite each fraction as an equivalent fraction
with a denominator of 12.
5
10
5 x 2
1
1 x 3
3




6 x 2
12
4
6
4 x 3
12
10
3
5
1
gt
so
gt
6
12
12
4
Solution The numbers in order from greatest to
least is 3, 2 2
5
1
6
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.
7
Coached Example Order these numbers from
greatest to least.
7
7
72 1 1.78
10
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 _____
gt _____ gt _____ gt _____ The numbers ordered from
greatest to least are _____, _____, _____, _____