Welcome to the understanding fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person's life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren't that difficult to master especially with the support of our wide selection of worksheets.
This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they'll probably let you know that it makes one delicious snack.
The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting... by the time students master the material on this page, operations of fractions will be a walk in the park.
General Use Printables
The black and white fraction circles can be used as a manipulative to compare fractions. Photocopy the worksheet onto an overhead projection slide. Use a pencil to lightly color the appropriate circle to represent the first fraction on the paper copy. Use a non-permanent overhead pen to color the appropriate circle to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.
Fraction strips can be laminated for durability and cut out to compare, order, add and subtract fractions. They are very useful for comparing fractions. You can also copy the fractions strips onto overhead projection slides and cut them out. Not only will they be durable, they will also be transparent which is useful when used in conjunction with paper versions (e.g. for comparing fractions).
Modeling Fractions Worksheets
Besides using the worksheets below, you can also try some more interesting ways of modeling fractions. Healthy snacks can make great models for fractions. Can you cut a cucumber into thirds? A tomato into quarters? Can you make two-thirds of the grapes red and one-third green?
Rectangular Fraction Models
Circle Fraction Models
Ratio and Proportion Worksheets
A small collection of math worksheets related to ratio and proportion. Please note that the picture ratio worksheets below are large and may take time to load if you are on a slower connection.
Comparing Simple Fractions Worksheets
Now we're getting into the nitty gritty of fractions. This is the first big road block that most students encounter, but you don't have to make this one a "stopper." There are many different strategies other than staring at the page that will help in comparing fractions. Try starting with something visual that will depict the fractions in question. We highly recommend our fraction strips (scroll up a bit). Using a straight edge like a ruler or book or folding will help students to easily see which fraction is greater or if they are equal. We should also mention that the things that are compared should be the same. Each fraction strip for example is the same size whereas if you took a third of a watermelon and half of a grape, the watermelon would probably win out.
Another strategy to use when comparing fractions is to use a number line and to use benchmarks like 0, 1, 1/2 to figure out where each fraction goes then see which one is bigger. Students actually do this one all the time since they can often compare fractions by recognizing that one is less than half and the other is greater than half. They might also see that one fraction is much closer to a whole than another fraction even though they might both be greater than a half.
We'll mention one other strategy, but there are more. This one requires a little bit more knowledge, but it works out well in the long run because it is a certain way of comparing fractions. Convert each fraction to a decimal and compare the decimals. Decimal conversions can be memorized (especially for the common fractions) calculated with long division or using a calculator or look-up table. We suggest the latter since using a look-up table often leads to mental recall.
Comparing Simple and Improper Fractions Worksheets
Comparing Simple, Improper and Mixed Fractions Worksheets
Ordering Fractions Worksheets a.k.a. Sorting Fractions
Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We've probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won't cut it. Try using some visuals to reinforce this important concept. Even though we've included number lines below, feel free to use your own strategies.
Ordering Fractions on a Number Line
Simplifying Fractions Worksheets
Learning how to simplify fractions makes a student's life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.