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Learn Fractions

Finally understand fractions, from pizza slices to dividing by 2/3.

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A fraction is a number that represents part of a whole, or more generally a division: 3/4 means 3 divided by 4. Fractions trip up many learners because the rules seem to change from operation to operation. You need a common denominator to add, but not to multiply, and dividing means multiplying by the reciprocal. Seeing fractions on a number line and with area models makes each rule make sense. Learnr builds a personalized fractions course and teaches it in short interactive lessons, moving from the meaning of a fraction to fluent calculation and conversion to decimals and percents.

How to learn Fractions, step by step

Understand fractions with pictures first. Draw fraction bars, circles and number lines to see that 3/4 is three parts of a whole split into four equal parts. Place fractions like 1/2, 2/3 and 5/4 on a number line to see they are just numbers.
Learn equivalent fractions and simplifying. Multiply or divide the top and bottom by the same number to get an equivalent fraction, and simplify by dividing by the greatest common factor. Shading area models shows why 2/4 and 1/2 are equal.
Compare fractions with confidence. Rewrite fractions over a common denominator, or compare with benchmarks like 1/2 and 1. Cross-multiplying is a quick check once you understand why it works.
Add and subtract with common denominators. Find the least common denominator, rewrite each fraction, then add the numerators only. Practice with mixed numbers too, including borrowing a whole when subtracting, as in 3 1/4 - 1 3/4.
Multiply and divide. Multiply numerators and denominators straight across, simplifying first when you can. To divide, multiply by the reciprocal of the divisor, and check the result with a picture, such as how many halves fit into 3.
Convert and practice in short sessions. Turn fractions into decimals by dividing and into percents by scaling to a denominator of 100, and memorize common ones like 1/8 = 0.125. A few minutes daily in Learnr keeps every rule in place.

What you'll learn

Explain what a fraction means and place fractions on a number line
Find equivalent fractions and simplify using the greatest common factor
Compare and order fractions with unlike denominators
Add, subtract, multiply and divide fractions and mixed numbers
Convert among fractions, decimals and percentages

What's inside your Fractions course

A sample path Learnr builds for Fractions. Your real course adapts to your goal and level.

1. What a fraction really means
2. Equivalent fractions and simplifying
3. Comparing and ordering fractions
4. Adding and subtracting fractions
5. Multiplying and dividing fractions
6. Mixed numbers, decimals and percentages

How long does it take to learn Fractions?

Most learners can understand and calculate with fractions confidently in about 3 to 6 weeks at 2 to 3 hours a week. Adults refreshing the topic often need only 1 to 2 weeks to rebuild the rules and practice them.

What you need before you start

Whole-number multiplication and division, including the times tables. Knowing how to find factors of a number makes simplifying much faster.

Common mistakes to avoid

Adding the denominators, as in 1/2 + 1/3 = 2/5. Rewrite both over a common denominator first, giving 3/6 + 2/6 = 5/6.
Flipping the wrong fraction when dividing. Keep the first fraction, change division to multiplication, and flip only the second.
Forgetting to simplify the final answer, or to convert an improper fraction to a mixed number when the problem asks for one.

How Learnr builds your course

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Fractions questions, answered

Why do you flip the second fraction when dividing?

Dividing by a number is the same as multiplying by its reciprocal. Asking how many 1/3s fit into 2 gives 6, which equals 2 × 3. The same logic works for any fraction.

Why do I need a common denominator to add but not to multiply?

Adding combines pieces, which only makes sense if the pieces are the same size. Multiplying takes a fraction of a fraction, like half of three-quarters, which works directly with the parts you have.