Welcome to the 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 and operations with 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?
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 & Ordering 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.
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.
Simplifying & Converting 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.
Operations with Fractions Worksheets
Welcome to the operations with fractions section where half of a fraction can sometimes be one! This section includes fractions worksheets for adding, subtracting, multiplying and dividing fractions including multiple operations and order of operations with fractions.
Although many people start with adding and subtracting fractions, we've started with multipying and dividing because it is less confusing operationally and can be less confusing conceptually if approached in the right way (see below). Adding and subtracting fractions, of course, requires that annoying common denominator, but make it easy on your students by first teaching the concept of equivalent fractions. Once students are familiar with the idea of equivalent fractions, the idea of finding fractions with common denominators for adding and subtracting becomes that much easier.
Near the end of the section, you will find some worksheets with mixed operations on one page and some order of operations with fractions worksheets. We've even included a few with decimals mixed in.
When you work with whole numbers, usually addition and subtraction come first, so why include multiplication and division first? The simple answer is that the algorithm for multiplying and dividing fractions is much easier. If your student(s) has mastered all of the above skills, however, there is no reason why you can't scroll down and start with addition and subtraction. Please DO spend a little time with the concept of multiplication of fractions; it will help them see what they are doing. The magic word in multiplication of fractions is, "of." For example what is two-thirds OF six? What is a third of a half? When you use the word, "of," it gets much easier to visualize fractions multiplication. Quick example: cut a loaf of bread in half, then cut the half into thirds. One-third of a half loaf of bread is the same as 1/3 x 1/2 and tastes delicious with butter.
Conceptually, dividing fractions is probably the most difficult of all the operations, but we're going to help you out. The algorithm for dividing fractions is just like multiplying fractions, but you find the inverse of the second fraction or you cross-multiply. This gets you the right answer which is extremely important especially if you're building a bridge. We told you how to conceptualize fraction multiplication, but how does it work with division? Easy! You just need to learn the magic phrase: "How many ____'s are there in ______? For example, in the question 6 ÷ 1/2, you would ask, "How many halves are there in 6?" It becomes a little more difficult when both numbers are fractions, but it isn't a giant leap to figure it out. 1/2 ÷ 1/4 is a fairly easy example. We'll leave the rest up to you.
Adding fractions is much easier if a student has a good understanding of what a fraction is and the concept of equivalent fractions. Students need to spend some time on modeling fractions (to know what they are) and learning the concept of equivalent fractions, so they are able to find common denominators. For those students who do not have the prerequisite knowledge, they will probably only be successful on the adding fractions with like denominators below. Students who do have a firm grasp on the idea of equivalent fractions will probably excel at the adding fractions with easy to find common denominators and find little challenge in the adding fractions worksheets with unlike denominators.
One strategy to use when adding mixed fractions is to convert the mixed fractions to improper fractions, complete the addition, then switch back. A better strategy which requires a little less brainpower is to look at the whole numbers and fractions separately. Add the whole numbers first. Add the fractions second. If the resulting fraction is improper, then it needs to be converted to a mixed number. The whole number portion can be added to the original whole number portion.
As with other order of operation worksheets, the fractions order of operations worksheets require some pre-requisite knowledge. If your students struggle with these questions, it probably has more to do with their ability to work with fractions than the questions themselves. Observe closely and try to pin point exactly what pre-requisite knowledge is missing then spend some time going over those concepts/skills before proceeding. Otherwise, the worksheets below should have fairly straight-forward answers and shouldn't result in too much hair loss.