Welcome to the operations with fractions page where half of a fraction can sometimes be one! This page 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 bottom of the operations with fractions worksheets page, you will find some worksheets with multiple operations on one page and some order of operations with fractions worksheets. We've even included a few with some decimals mixed in.
Multiplying Fractions Worksheets
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.
Multiplying 2 Fractions
Multiplying 3 Fractions
Dividing Fractions Worksheets
Conceptually, this is probably the most difficult, 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.
Dividing 2 Fractions
Dividing 3 Fractions
Adding Fractions Worksheets
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.
Adding Fractions with Like Denominators
Adding Fractions with Easy to Find Common Denominators
Adding Fractions with Unlike Denominators
Adding Mixed Fractions Worksheets
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.
Subtracting Fractions Worksheets
Subtracting Fractions with Like Denominators
Subtracting Fractions with Easy to Find Common Denominators
Subtracting Fractions with Unlike Denominators
Subtracting Mixed Fractions Worksheets
Multiple Operations with Fractions Worksheets
Fractions Worksheets -- Order of Operations
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.