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.

**194 views this week**) Adding and Subtracting Fractions -- No Mixed Fractions (

**129 views this week**) Converting Mixed Fractions to Improper Fractions (

**117 views this week**) Simplifying Proper Fractions to Lowest Terms (Easier Questions) (

**104 views this week**) Adding and Subtracting Mixed Fractions (

**103 views this week**)

## General Use Fractions Printables

**Fraction Circles**

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**

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?

**Modeling** fractions **with groups of shapes**

Fractions can represent parts of a group or parts of a whole. In these worksheets, fractions are modeled as parts of a group.

**Modeling** fractions **with rectangles**

**Modeling** fractions **with circles**

## Ratio and Proportion Worksheets

**Picture ratios**

More picture ratios can be found on holiday and seasonal pages. Try searching for picture ratios to find more.

**Equivalent fractions**

The equivalent fractions models worksheets include only the "baking fractions" in the A versions. To see more difficult and varied fractions, please choose the B to J versions after loading the A version.

Formerly: Find the Missing Number Are These Fractions Equivalent? (Multiplier 2 to 5) Are These Fractions Equivalent? (Multiplier 5 to 15) Equivalent Fractions

**Models**Equivalent Fractions

**Models**with the

**Simplified Fraction First**Equivalent Fractions

**Models**with the

**Simplified Fraction Second**

**Equivalent ratios**

## Comparing & Ordering Fractions Worksheets

**Comparing simple** fractions

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.

**Comparing Simple and Improper** Fractions

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.

**Comparing Simple, Improper and Mixed** Fractions

Another strategy for comparing fractions is to 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.

**Ordering** fractions **on a Number Line**

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.

**Easy Denominators to 10**on a Number Line Ordering Fractions with

**Easy Denominators to 24**on a Number Line Ordering Fractions with

**Easy Denominators to 60**on a Number Line Ordering Fractions with

**Easy Denominators to 100**on a Number Line Ordering Fractions with

**Easy Denominators to 10 + Negatives**on a Number Line Ordering Fractions with

**Easy Denominators to 24 + Negatives**on a Number Line Ordering Fractions with

**Easy Denominators to 60 + Negatives**on a Number Line Ordering Fractions with

**Easy Denominators to 100 + Negatives**on a Number Line Ordering Fractions with

**All Denominators to 10**on a Number Line Ordering Fractions with

**All Denominators to 24**on a Number Line Ordering Fractions with

**All Denominators to 60**on a Number Line Ordering Fractions with

**All Denominators to 100**on a Number Line Ordering Fractions with

**All Denominators to 10 + Negatives**on a Number Line Ordering Fractions with

**All Denominators to 24 + Negatives**on a Number Line Ordering Fractions with

**All Denominators to 60 + Negatives**on a Number Line Ordering Fractions with

**All Denominators to 100 + Negatives**on a Number Line

**Ordering** fractions

The ordering fractions worksheets in this section do not include a number line, to allow for students to use various sorting strategies.

**Like Denominators**Ordering Positive Fractions with

**Like Numerators**Ordering Positive Fractions with

**Like Numerators or Denominators**Ordering Positive Fractions

**with Proper Fractions Only**Ordering Positive Fractions

**with Improper Fractions**Ordering Positive Fractions

**with Mixed Fractions**Ordering Positive Fractions

**with Improper and Mixed Fractions**Ordering Positive and

**Negative**Fractions with

**Like Denominators**Ordering Positive and

**Negative**Fractions with

**Like Numerators**Ordering Positive and

**Negative**Fractions with

**Like Numerators or Denominators**Ordering Positive and

**Negative**Fractions

**with Proper Fractions Only**Ordering Positive and

**Negative**Fractions

**with Improper Fractions**Ordering Positive and

**Negative**Fractions

**with Mixed Fractions**Ordering Positive and

**Negative**Fractions

**with Improper and Mixed Fractions**

## Simplifying & Converting Fractions Worksheets

**Rounding** fractions

Rounding fractions helps students to understand fractions a little better and can be applied to estimating answers to fractions questions. For example, if one had to estimate 1 4/7 × 6, they could probably say the answer was about 9 since 1 4/7 is about 1 1/2 and 1 1/2 × 6 is 9.

**Fractions**to the

**Nearest Whole**with

**Helper Lines**Rounding

**Mixed Numbers**to the

**Nearest Whole**with

**Helper Lines**Rounding

**Fractions**to the

**Nearest Half**with

**Helper Lines**Rounding

**Mixed Numbers**to the

**Nearest Half**with

**Helper Lines**Rounding

**Fractions**to the

**Nearest Whole**Rounding

**Mixed Numbers**to the

**Nearest Whole**Rounding

**Fractions**to the

**Nearest Half**Rounding

**Mixed Numbers**to the

**Nearest Half**

**Simplifying** fractions

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.

**Converting** between improper and mixed fractions

**Converting** between fractions, decimals, percents, and ratios

**Converting Fractions**to Decimals, Percents and Part-to-

**Part**Ratios (

**Terminating**Decimals Only)

**Converting Fractions**to Decimals, Percents and Part-to-

**Whole**Ratios (

**Terminating**Decimals Only)

**Converting Decimals**to Fractions, Percents and Part-to-

**Part**Ratios (

**Terminating**Decimals Only)

**Converting Decimals**to Fractions, Percents and Part-to-

**Whole**Ratios (

**Terminating**Decimals Only)

**Converting Percents**to Fractions, Decimals and Part-to-

**Part**Ratios (

**Terminating**Decimals Only)

**Converting Percents**to Fractions, Decimals and Part-to-

**Whole**Ratios (

**Terminating**Decimals Only)

**Converting Part-to-Part Ratios**to Fractions, Decimals and Percents (

**Terminating**Decimals Only)

**Converting Part-to-Whole Ratios**to Fractions, Decimals and Percents (

**Terminating**Decimals Only)

**Converting Various**Fractions, Decimals, Percents and Part-to-

**Part**Ratios (

**Terminating**Decimals Only)

**Converting Various**Fractions, Decimals, Percents and Part-to-

**Whole**Ratios (

**Terminating**Decimals Only)

**Converting Fractions**to Decimals, Percents and Part-to-

**Part**Ratios

**Converting Fractions**to Decimals, Percents and Part-to-

**Whole**Ratios

**Converting Decimals**to Fractions, Percents and Part-to-

**Part**Ratios

**Converting Decimals**to Fractions, Percents and Part-to-

**Whole**Ratios

**Converting Percents**to Fractions, Decimals and Part-to-

**Part**Ratios

**Converting Percents**to Fractions, Decimals and Part-to-

**Whole**Ratios

**Converting Part-to-Part Ratios**to Fractions, Decimals and Percents

**Converting Part-to-Whole Ratios**to Fractions, Decimals and Percents

**Converting Various**Fractions, Decimals, Percents and Part-to-

**Part**Ratios

**Converting Various**Fractions, Decimals, Percents and Part-to-

**Whole**Ratios

**Converting Various**Fractions, Decimals, Percents and Part-to-

**Part**Ratios with

**7ths and 11ths**

**Converting Various**Fractions, Decimals, Percents and Part-to-

**Whole**Ratios with

**7ths and 11ths**(OLD) Converting Fractions, Decimals, Percents and Ratios

## Operations with Fractions Worksheets

**Multiplying Fractions**

Multiplying fractions is usually less confusing operationally than any other operation and can be less confusing conceptually if approached in the right way. The algorithm for multiplying is simply multiply the numerators then multiply the denominators. The magic word in understanding the 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. 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.

**2**Fractions Multiplying

**2**Fractions (Some Whole Numbers) Multiplying

**2**Fractions (Some Mixed) Multiplying

**2**Mixed Fractions Multiplying

**3**Fractions Multiplying

**3**Fractions (Some Whole Numbers) Multiplying

**3**Fractions (Some Mixed) Multiplying

**3**Mixed Fractions

**Dividing Fractions**

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, especially if you think in terms of U.S. or Canadian coins. How many quarters are there in a half dollar?

**2**Fractions Dividing

**2**Fractions (Some Whole Numbers) Dividing

**2**Fractions (Some Mixed) Dividing

**2**Mixed Fractions Dividing

**3**Fractions Dividing

**3**Fractions (Some Whole Numbers) Dividing

**3**Fractions (Some Mixed) Dividing

**3**Mixed Fractions

**Adding** Fractions

Adding fractions requires the annoying common denominator. Make it easy on your students by first teaching the concepts of equivalent fractions and least common multiples. Once students are familiar with those two concepts, the idea of finding fractions with common denominators for adding becomes that much easier. Spending time on modeling fractions will also help students to understand fractions addition. Relating fractions to familiar examples will certainly help. For example, if you add a 1/2 banana and a 1/2 banana, you get a whole banana. What happens if you add a 1/2 banana and 3/4 of another banana?

**Like Denominators**(Simple Fraction Sums) Adding Fractions with

**Like Denominators**(Mixed Fraction Sums) Adding Fractions with

**Like Denominators**(Improper Fractions Included in Questions) Adding Proper Fractions with

**Easy to Find Common Denominators**Adding Proper Fractions with

**Easy to Find Common Denominators**(Mixed Fraction Results) Adding Proper and Improper Fractions with

**Easy to Find Common Denominators**(Mixed Fraction Results) Adding Proper Fractions with

**Unlike Denominators**Adding Proper Fractions with

**Unlike Denominators**(Mixed Fraction Results) Adding Proper and Improper Fractions with

**Unlike Denominators**(Mixed Fraction Results) Adding Proper Fractions

**Vertically**with

**Denominators from 2 to 9**

**Adding Mixed Fractions** Worksheets

A common strategy to use when adding mixed fractions is to convert the mixed fractions to improper fractions, complete the addition, then switch back. Another 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

There isn't a lot of difference between adding and subtracting fractions. Both require a common denominator which requires some prerequisite knowledge. The only difference is the second and subsequent numerators are subtracted from the first one. There is a danger that you might end up with a negative number when subtracting fractions, so students might need to learn what is means in that case. When it comes to any concept in fractions, it is always a good idea to relate it to a familiar or easy-to-understand situation. For example, 7/8 - 3/4 = 1/8 could be given meaning in the context of a race. The first runner was 7/8 around the track when the second runner was 3/4 around the track. How far ahead was the first runner? (1/8 of the track).

**Like Denominators**Subtracting Im/Proper Fractions with

**Like Denominators**Subtracting Im/Proper Fractions with

**Like Denominators**(Mixed Fraction Results) Subtracting Proper Fractions with

**Easy to Find Common Denominators**Subtracting Im/Proper Fractions with

**Easy to Find Common Denominators**Subtracting Im/Proper Fractions with

**Easy to Find Common Denominators**(Mixed Fraction Results) Subtracting Proper Fractions with

**Unlike Denominators**Subtracting Im/Proper Fractions with

**Unlike Denominators**Subtracting Im/Proper Fractions with

**Unlike Denominators**(Mixed Fraction Results)

**Subtracting Mixed Fractions** Worksheets

## Various Operations Fractions Worksheets

Mixing up the signs on operations with fractions worksheets makes students pay more attention to what they are doing and allows for a good test of their skills in more than one operation.

**Adding and subtracting** fractions

**Multiplying and dividing** fractions

**Mixed operations** with fractions

**Two Fractions**Including

**Some Improper**Fractions All Operations with

**Two Fractions**Including

**Some Negative**and

**Some Improper**Fractions All Operations with

**Three Fractions**Including

**Some Improper**Fractions All Operations with

**Three Fractions**Including

**Some Negative**and

**Some Improper**Fractions

### Operations with **Negative** fractions

Although some of these worksheets are single operations, it should be helpful to have all of these in the same location. There are some special considerations when completing operations with negative fractions. It is usually very helpful to change any mixed numbers to an improper fraction before proceeding. It is important to pay attention to the signs and know the rules for multiplying positives and negatives (++ = +, +- = -, -+ = - and -- = +).

**Adding**Negative Fractions

**to Sixths**

**Adding**Negative Fractions

**to Twelfths**

**Adding**Negative

**Mixed**Fractions

**to Sixths**

**Adding**Negative

**Mixed**Fractions

**to Twelfths**

**Subtracting**Negative Fractions

**to Sixths**

**Subtracting**Negative Fractions

**to Twelfths**

**Subtracting**Negative

**Mixed**Fractions

**to Sixths**

**Subtracting**Negative

**Mixed**Fractions

**to Twelfths**

**Multiplying**Negative Fractions

**to Sixths**

**Multiplying**Negative Fractions

**to Twelfths**

**Multiplying**Negative

**Mixed**Fractions

**to Sixths**

**Multiplying**Negative

**Mixed**Fractions

**to Twelfths**

**Dividing**Negative Fractions

**to Sixths**

**Dividing**Negative Fractions

**to Twelfths**

**Dividing**Negative

**Mixed**Fractions

**to Sixths**

**Dividing**Negative

**Mixed**Fractions

**to Twelfths**

## Order of Operations with Fractions Worksheets

Order of operations with fractions worksheets with both positive and negative fractions options and a variety of complexity.

### Order of Operations with **Fractions**

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.

**2-Step**Order of Operations with Positive Fractions

**3-Step**Order of Operations with Positive Fractions

**4-Step**Order of Operations with Positive Fractions

**5-Step**Order of Operations with Positive Fractions

**6-Step**Order of Operations with Positive Fractions

**2-Step**Order of Operations with Positive Fractions

**(No Exponents)**

**3-Step**Order of Operations with Positive Fractions

**(No Exponents)**

**4-Step**Order of Operations with Positive Fractions

**(No Exponents)**

**5-Step**Order of Operations with Positive Fractions

**(No Exponents)**

**6-Step**Order of Operations with Positive Fractions

**(No Exponents)**

**2-Step**Order of Operations with Positive &

**Negative**Fractions

**3-Step**Order of Operations with Positive &

**Negative**Fractions

**4-Step**Order of Operations with Positive &

**Negative**Fractions

**5-Step**Order of Operations with Positive &

**Negative**Fractions

**6-Step**Order of Operations with Positive &

**Negative**Fractions