These guides explain why fractions work, not just how to calculate them. Choose by what you are missing: understanding what a fraction is, avoiding a mistake in an operation, moving to decimals, or applying fractions to a sharing problem. The table points you to the guide that fits your question.
| My question | Guide | What you will practice |
|---|---|---|
| I don't know what a fraction represents | What fractions are | Reading a fraction as parts of a whole |
| My sum gives a strange result | Why denominators are not added | 1/2 + 1/3 = 5/6 |
| Dividing by a fraction confuses me | Dividing by a fraction | 3 ÷ 1/2 = 6 |
| I can't tell whether to use GCF or LCM | GCD vs. LCM | GCD(12, 18) = 6 and LCM(12, 18) = 36 |
| I want to know whether a decimal ends | Terminating or repeating decimal | Deciding whether the decimal of a fraction ends or repeats |
| I have negative signs | Negative fractions | Working with negative fractions without losing the sign |
Find your situation in the first column and open the guide in the second. If you want the result rather than the explanation, the fraction calculator gives it with the steps.
Four paths by what you need
Each path gathers a few guides, in the order they are best read. The other related pages appear at the end, in the “More resources” block.
Starting from zero
Read what fractions are first, then numerator and denominator. With those two you can read 7/8 as seven parts of a whole divided into eight. Continue with the types of fractions and how to draw fractions, which let you see the size before you calculate.
Solving an operation without mistakes
Start with the common mistakes, because they tend to happen at the same step. Then pick the operation that trips you up: why denominators are not added, why dividing by a fraction can increase a number or multiplying by a fraction less than one. When signs appear, move on to negative fractions, and finish with how to check an answer.
Converting and comparing decimals
Here the order goes from the rule to the lookup table and then to the explanation. When a fraction gives a terminating or repeating decimal is decided by the denominator. The fraction, decimal and percent table is for looking things up, and terminating and repeating decimals explains why 0.999… equals 1. The tools for this path are in conversions.
Applying fractions to problems
To share an amount, proportional sharing with fractions goes from the weight of each part to the share each person gets. If the problem is about turns or groupings, GCD and LCM word problems helps you decide which calculation it asks for. For recipes and measurements, see fractions in recipes and measurements, and for practice with complete solutions, the worked fraction exercises.
An example of how to use a guide
Worked example: 1/6 + 3/4
You have 1/6 cup of juice and add 3/4 cup. How much juice is there?
- Find a common denominator. The LCM of 6 and 4 is 12.
- Convert each fraction. 1/6 = 2/12 and 3/4 = 9/12.
- Add the numerators. 2/12 + 9/12 = 11/12.
Result: 11/12 cup.
Check: 11/12 − 3/4 = 11/12 − 9/12 = 2/12 = 1/6, the other addend.
The guide that explains this step is why denominators are not added, and GCD vs. LCM clarifies why the LCM is used here.
When to move from the guide to the tool
A guide teaches the why; a calculator saves the work. The most useful routine is to read the explanation, solve an example by hand, and then compare it with the fraction calculator. If the result does not match, go back to the step where your work departs from the example. When you have an exercise and your own answer, fraction answer checking tells you whether the value matches, and for new exercises with solutions there is the worksheet generator.
If you teach fractions, how to teach fractions step by step proposes a sequence that runs from the unit to operations. For a term you don’t remember, the fraction glossary defines them all.
Four questions to choose a path
- Can you explain with a drawing what 5/8 means? If not, start with the first path.
- Do you know how to do the operation, but the result comes out wrong? Go to the second path.
- Does your problem start with a decimal? Go to the third path.
- Does it start with a sharing problem or a word problem? Go to the fourth path.
Each answer points to a single path, so start with the first question you cannot answer with confidence.
Guides that are not in the paths
If you are looking for a topic that is not in the paths, such as algebraic fractions and domain or why a fraction cannot have a zero denominator, start with those two. The first covers when an expression with letters has no value, and the second explains why division by zero gives no result. The other related pages are grouped by type in the “More resources” block that follows this page; some carry a line saying what they solve.