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1,100 possible mastery points

About this unit

From cooking measurements to geometry, fractions are all around us. By understanding how the numerator and denominator work together, you'll be able to break down numbers into smaller parts, compare different fractions, and get a grasp on concepts like equivalent fractions.

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Understand fractions | Arithmetic | Math | Khan Academy

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From cooking measurements to geometry, fractions are all around us. By understanding how the numerator and denominator work together, you'll be able to break down numbers into smaller parts, compare different fractions, and get a grasp on concepts like equivalent fractions.

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Slice a pizza, and we get fractions:

The top number says how many slices we have.
The bottom number says how many equal slices the whole pizza was cut into.

Have a try yourself:

Equivalent Fractions

Some fractions may look different, but are really the same, for example:

=

=

(Four-Eighths)

(Two-Quarters)

(One-Half)

=

=

It is usually best to show an answer using the simplest fraction ( in this case ). That is called Simplifying, or Reducing the Fraction

Numerator / Denominator

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

You just have to remember those names! (If you forget just think "Down"-ominator)

Adding Fractions

It is easy to add fractions with the same denominator (same bottom number):

Another example:

Five-eighths plus one-eighth equals six-eighths, equals three-quarters

Adding Fractions with Different Denominators

But what about when the denominators (the bottom numbers) are not the same?

Three-eighths plus one-quarter equals ... what?

We must somehow make the denominators the same.

Three-eighths plus two-eighths equals five-eighths

There are two popular methods to make the denominators the same:

(They both work nicely, use the one you prefer.)

Other Things We Can Do With Fractions

We can also:

Visit the Fractions Index to find out even more.

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The top number says how many slices we have. The bottom number says how many equal slices the whole pizza was cut into. Some fractions may look different, but are really the same, for example: = = (Four-Eighths) (Two-Quarters) (One-Half) = = It is usually best to show an answer using the simplest fraction ( in this case ).

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Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

Mixed Numbers Calculator

Simplify Fractions Calculator

Decimal to Fraction Calculator

Fraction to Decimal Calculator

Big Number Fraction Calculator

Use this calculator if the numerators or denominators are very big integers.

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction of

, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Addition:

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.

Subtraction:

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

Multiplication:

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

Division:

The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is simply

. When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction would therefore be . Refer to the equations below for clarification.

Simplification:

It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms.

for example, is more cumbersome than . The calculator provided returns fraction inputs in both improper fraction form as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.

Converting between fractions and decimals:

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 10 ¹, the second 10 ², the third 10 ³, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 10 ⁴, or 10,000. This would make the fraction

, which simplifies to , since the greatest common factor between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction

for example. To convert this fraction into a decimal, first convert it into the fraction of . Knowing that the first decimal place represents 10⁻¹, can be converted to 0.5. If the fraction were instead , the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.

Common Engineering Fraction to Decimal Conversions

In engineering, fractions are widely used to describe the size of components such as pipes and bolts. The most common fractional and decimal equivalents are listed below.

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Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator. Use this calculator if the numerators or denominators are very big integers.

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A Half can be written...

A Quarter can be written...

Here, have a play with it yourself:

numbers/images/ani-frac-num-pct.js

Example Values

Here is a table of commonly used values shown in Percent, Decimal and Fraction form:

Conversions!

From Percent to Decimal

To convert from percent to decimal divide by 100 and remove the % sign.

An easy way to divide by 100 is to move the decimal point 2 places to the left:

From Percent

To Decimal

move the decimal point 2 places to the left

Don't forget to remove the % sign!

From Decimal to Percent

To convert from decimal to percent multiply by 100%

An easy way to multiply by 100 is to move the decimal point 2 places to the right:

From Decimal

To Percent

move the decimal point 2 places to the right

Don't forget to add the % sign!

From Fraction to Decimal

To convert a fraction to a decimal divide the top number by the bottom number:

Divide 2 by 5: 2 ÷ 5 = 0.4

From Decimal to Fraction

To convert a decimal to a fraction needs a little more work.

Example: To convert 0.75 to a fraction

From Fraction to Percentage

To convert a fraction to a percentage divide the top number by the bottom number, then multiply the result by 100%

First divide 3 by 8: 3 ÷ 8 = 0.375

Then multiply by 100%: 0.375 × 100% = 37.5%

From Percentage to Fraction

To convert a percentage to a fraction, first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).

Example: To convert 80% to a fraction

881, 1305,882, 1306,883, 1307,884, 1308,885, 1309,886, 1310

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Decimals, Fractions and Percentages are just different ways of showing the same value

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Here you will find our selections of Fractions Decimals Percents Worksheets to help you to learn and practice converting between fractions, decimals and percentages.

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Ceramics video tutorial: How to make a clay pinch pot

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Get your Great Pottery Throw Down applications at the ready! Watch this video tutorial and learn how to make a simple clay pinch pot / thumb pot!

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Irish vocabulary for Topaic na Seachtaine ‘Éadaí’ (Clothes). Learn Irish online at LetsLearnIrish.com

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The Most Important Revolutions That Shaped World History

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These five revolutions are particularly noteworthy for their long-lasting impact on the world. Through bloodshed came change, and a new future for these nations.

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In 1789 the people of France began the French Revolution. The revolution brought down their king and made France a republic-a country ruled by the people. This republic did...

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Kids learn about the history of the French Revolution including causes, major events, Reign of Terror, National Assembly, symbols, famous people, Storming of the Bastille, and facts. Educational article for students, schools, and teachers.

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How are sounds made? – KS2 Science curriculum - BBC Bitesize

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Learn how sounds are made with these interactive learning resources for KS2 Science students aged 7-11 from BBC Bitesize.

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Heat is a form of energy. Heat flows from hot objects to cool objects. It flows from one object to another because of their difference in temperature. The cool object absorbs the energy and becomes warmer.

Objects are made of particles, or bits, called molecules. Molecules are always in motion. As an object is heated, the molecules in the object move faster. When this happens, the temperature of the object rises.

Heat travels in three ways: by conduction, by convection, and by radiation. Conduction is the flow of heat inside an object. It is also the flow of heat between objects in contact with each other. An example is the flow of heat from a hot frying pan to food placed on the pan to cook.

Convection is the flow of heat caused by the motion of a liquid or a gas. An example is the heating of water in a teakettle. As water is heated, the molecules that make up the water rise and the heat spreads.

Heat radiation is the flow of heat between objects that are not in contact with each other. An example is the heat felt by someone standing a distance away from a hot stove.

Radiation from the Sun gives Earth most of its heat. Energy from the Sun's radiation is stored in such fuels as coal, oil, gas, and wood. These fuels can be burned to provide more heat.

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Heat is a form of energy. Heat flows from hot objects to cool objects. It flows from one object to another because of their difference in temperature. The cool object absorbs...

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This website offers easy interactive spelling practice for kids in early elementary years (grades 1, 2, 3 and 4). Just type, listen and learn English - learning spelling can be as simple as that!

In this page you set up which words to test students on. The next page - after you hit the "Online Spelling Test" button - lets the kids tackle the spelling test and check their performance.

This free spelling website acts like an online computer program, in which you can create your own spelling lists, and have word games with your own words.
All the games and the other educational interactive activities on this website are totally free!

The Word's Pronunciation

You can also use this website to learn how to pronounce English words. Each word is pronounced slowly and clearly, stressing and emphasizing each syllable and consonant. This makes it great for ESL students and special education students as well, helping to discover new English words and their correct pronunciation.

The Spelling Games & Activities

Online Spelling Test

This is a simple test in which you hear the words of your list in random order, and type them inside the text boxes. Do your best to spell them correctly. At the end, you can press the "Check" button to see how well you have done. If you made a mistake, you can click a mistaken word to see its correct form. You can also ask to repeat the test with only the mistaken words.

Practice Your Words

This online practice will guide you step by step until you know how to write each word correctly just by hearing it. It consists of three phases: in the first phase, the letters to type are highlighted on the keyboard. in the second phase the word will still be presented, and you will copy it. In the third phase, you will type it from solely hearing it.

Reading With Spaceships & Reading With Balloons

These are two similar games, one in is more action themed, and the other is calmer. They practice reading the words and matching them to the words you hear. It's an easy reading activity, best for kids in 1st grade and 2nd grade.

Spelling Sharks

This is an action online spelling game. When you type correctly the words you hear, you can eliminate the sharks that are threatening the goldfish. The typing is under time pressure, yet you can press the "clue" button to have the word flashed on the screen. This activity can be challenging, and is more suitable for kids in 3rd grade and 4th grade.

Hangman

This is a classic hangman game, using your own words. It's unique because you can actually hear the hidden words.

Word Search Puzzle

Immediately create a challenging online word search puzzle from your own list of words. After every word you find, you will hear it pronounced. The puzzles are dynamically created, and can sometimes be challenging even for kids in 5th grade and 6th grade.

The Spelling Lists

The lists are arranged in stages that coordinate to the children's development through spelling patterns, also called features.

The beginning lists for first graders allow the kids to approach the words one sound at a time (i.e. initial consonants), to then building more of a sight word vocabulary (i.e. word families).

Moving on from there, learners in second grade are able to chunk parts of words and process them more fluently when they read (i.e. consonant blends).

Third graders continue the fluency of reading while they explore the meanings of words (i.e. silent consonants), while fourth graders can handle more complex spelling patterns (i.e. double consonant with e-drop).

Of course, a student may overlap in stages, for instance, a second grader may still need some work on a few "first grade" features, or may dabble in some third grade features. They are merely an average "snapshot" for students in elementary school.

In addition to the lists for each grade level, there are many "themed" lists for students of all ages to enjoy (themes such as September, Halloween, Winter, Earth Day, Science Day etc.)

Spelling and studying words ultimately promotes a greater interest in reading and writing. When a child has word understanding and vocabulary knowledge, all aspects of Language Arts are enhanced.

Instructions

Which English words would you like to study? Type them into the empty spaces above. Once you do, you can click on the "Listen" button to hear how the word you typed is pronounced.

Sometimes there is more than one way to pronounce a word - for example, "read" sounds different in the past: "I read this book yesterday" to the way it sounds in the future: "I will read this book tomorrow". In this case you can hit the "Alternate" button to switch between the different pronunciations and choose the right one.

You can also choose from the word lists we've prepared already in the drop-down menu.

When you have finished adding words, choose an activity from one of the green buttons.
The spelling list will appear for the students. They should read it carefully and, when ready, start the activity.

When finished, the students will have the option to restart the activity or to exit to the main menu. In most cases, they will also get the option to repeat the activity with only the words they had trouble with.

Happy learning!

Comments & Feedback

Do you have a word you would like to add to those already recorded?
Teachers and parents are welcome to send their word requests to my email at [email protected] and I'll be happy to work on it. You can also contact me with questions, comments and suggestions.

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Free Online Spelling Training & Games for Grades 1, 2, 3 and 4

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Fun interactive spelling games for kids in early elementary years (grades 1, 2, 3 and 4). Type, listen and learn English - preparing to your spelling test can be as simple as that! A free online website.