This document provides guidance on ordering fractions and decimals from smallest to largest. It discusses: - Thinking of the number line from left to right, with numbers getting larger to the right and smaller to the left. - Comparing decimals first, then fractions, using benchmarks like 0, 1/2, and 1 to think about where fractions fall. - Tips like using unit fractions to compare fractions, thinking of fractions as portions of a whole to compare their sizes, and drawing a number line to visualize where negatives and positives fall in relation to each other. - Examples are provided to demonstrate the techniques. Key fraction-decimal equivalents are highlighted to memorize for comparisons.

1. Skill #1 Ordering Fractions and Decimals
Think about the number line as you plan to put numbers in order from smallest to largest.
Remember that numbers get larger as you move to the right and get smaller as you move
to the left.
Question: Put these numbers in order from smallest to largest.
0.38 1/10 -0.45 -2/3 7/8
How would you think about this? Use the ideas on the pages 48, 49, and 50 in the
Book.

2. Think about decimals first.
Answers. 0.2 0.3 0.5 0.8
0.058 0.36 0.375 0.4

3. 0.4 is bigger than 0.376 0.1 is bigger than 0.089

4. Next think about fractions. Use ½, 0, and 1 as benchmarks.
Try to think if the number is closer to 0, ½, or 1. Use decimal equivalents to help.
Sometimes it helps to be able to visualize how to divide the distance between 0 and 1
on the number line. In a problem, you can sometimes “eyeball” where a number lands.

5. Sometimes it is helpful to use “unit fractions” (have 1 for the top number).
Think about pizza slices pictured below. 1/8 is a smaller slice (and thus a smaller number
than ¼. On the number line, 1/8 would be on the left of ¼ because it is smaller.
Generally, if the top number is one, the larger the bottom
number, the smaller the value of the fraction. This can help you
place a fraction on the number line.

6. For other fractions consider whether they are closer to 0, ½, or 1. Think of ways to say
½ other than ½. 2/4, 3/6, 4/8, etc. For odd numbered denominators, think like this.
3.5/7 2.5/5 1.5/3 This gives you a way to decide if a fraction is more or less than
½ even if its bottom number is odd. Say you had to decide about 4/9. 4.5/9 is the
same as ½. So, 4/9 would be less than ½ and would be to the right of ½ on the
number line.

7. 0 1/2 1
.21 ¼ 2/3 .8 5/6
Why? Think about money. 0.21 is less than a quarter (0.25) or ¼. 2/3 I just estimated
as 2/3 of the distance between 0 and 1. Think about 0.8 as 80 cents. 5/6 is just a small
sliver shy of 1 (6/6) so 5/6 is very close to 1. Actually, I made the 0.8 and 5/6 too close
together. That will not happen on the test. You will be able to tell more easily.

8. 0 .5 1
0.00099 1/8 .58 3.4 8/9
Why? 0.00099 is practically 0. 1/8 is like the 1/8 slice of pizza – not much bigger than
0. 0.58 is just a little more than 0.5 or ½. ¾ is half way between ½ and 1 (like 3 quarters
of a dollar (0.75). 8/9 is just 1/9 (a small amount) less than 1 (9/9).

9. Make sure you can think about numbers on the negative side of 0.
-1 -.5 0
-.8 -1/2 -.30 -1/4 (-.25)
Pay attention to how the numbers are behaving on the left of 0.

10. I would learn the fraction/decimal equivalents on page 50 in the book to help
Those are very common and will help in other parts of the test too.
Be prepared for negatives too.
First draw out a number line from say -1 to +1 and put the decimal numbers on
the number line. Put .50 and -.5 on it as benchmarks.
-1 -.50 0 .50 +1
Expect a mixture of fractions and decimals with some negatives.
Sample test question: Put in order from smallest to largest.
0.4 -0.7 4/5 1/8 -0.889 -1/4
-1 0 1
-0.889 -.7 -1/4 0.4 4/5

11. Learn these!!