Fraction Calculator
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Mixed Numbers Calculator
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Simplify Fractions Calculator
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Decimal to Fraction Calculator
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Fraction to Decimal Calculator
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Big Number Fraction Calculator
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🔹 Introduction to Fractions
In mathematics, a fraction represents a part of a whole. It is composed of two parts: the numerator and the denominator. The numerator indicates how many parts are considered, while the denominator shows the total number of equal parts that form the whole.
For example, in the fraction 3/8, the numerator is 3, and the denominator is 8. Imagine a pie cut into 8 equal slices — if 3 slices are taken, the fraction representing the portion is 3/8. The denominator of a fraction must never be 0, as this would make the fraction undefined.
Fractions can be converted to decimal form by dividing the numerator by the denominator.
| Fraction | Numerator | Denominator | Example Description |
|---|---|---|---|
| 1/4 | 1 | 4 | 1 part out of 4 (25% of the whole) |
| 3/8 | 3 | 8 | 3 parts out of 8 (37.5% of the whole) |
| 5/8 | 5 | 8 | 5 parts out of 8 (62.5% of the whole) |
For a deeper explanation of fractions, check out Khan Academy - Fractions.
🔹 Adding Fractions
Adding fractions requires that they have a common denominator. The simplest way to achieve this is by multiplying the denominators of all fractions involved and adjusting the numerators accordingly. Alternatively, using the least common multiple (LCM) of the denominators is more efficient and typically results in a simplified fraction.
For example, consider adding 1/4 + 1/6 + 1/2:
| Method | Steps | Result |
|---|---|---|
| Multiply denominators | (1×6×2 + 1×4×2 + 1×4×6)/(4×6×2) | 44/48 = 11/12 |
| LCM | (1×3/12) + (1×2/12) + (1×6/12) | 11/12 |
Learn more about adding fractions at Math is Fun - Adding Fractions.
🔹 Subtracting Fractions
Subtracting fractions works much like addition — a common denominator is needed before you can subtract the numerators. You can either multiply denominators or find the least common multiple (LCM) for a cleaner result.
Example: 3/4 - 1/6
| Method | Steps | Result |
|---|---|---|
| Multiply denominators | (3×6 - 1×4)/(4×6) = (18 - 4)/24 | 14/24 = 7/12 |
| LCM (12) | (3×3/12) - (1×2/12) = (9 - 2)/12 | 7/12 |
For more techniques, see Math is Fun - Subtracting Fractions.
🔹 Multiplying Fractions
Multiplying fractions is simple compared to addition or subtraction because you do not need a common denominator. Just multiply the numerators together to get the new numerator, and the denominators together to get the new denominator. The result should then be simplified if possible.
Example: 3/4 × 1/6
= (3 × 1) / (4 × 6)
= 3 / 24
= 1 / 8
🔹 Dividing Fractions
Dividing fractions involves multiplying the first fraction (the dividend) by the reciprocal of the second fraction (the divisor). The reciprocal of a fraction is created by swapping its numerator and denominator.
Example: 3/4 ÷ 1/6
= 3/4 × 6/1
= 18/4
= 9/2
This result can also be expressed as a mixed number: 9/2 = 4 1/2.
🔹 Simplifying Fractions
Simplifying fractions means expressing the fraction in its lowest terms. This is done by dividing both the numerator and denominator by their greatest common divisor (GCD). A simplified fraction is easier to work with and interpret.
Example: 220/440
The GCD of 220 and 440 is 220.
= (220 ÷ 220) / (440 ÷ 220)
= 1/2
🔹 Converting Fractions to Decimals
Converting a fraction to a decimal is simple: divide the numerator by the denominator. This can be done manually or using a calculator.
Example: 1/8
= 1 ÷ 8
= 0.125
🔹 Converting Decimals to Fractions
To convert a decimal to a fraction, write the decimal as the numerator over a power of 10 based on the decimal places, then simplify if possible.
Example: 0.375
= 375/1000
Simplify by dividing numerator and denominator by 125:
= 3/8
🔹 Frequently Asked Questions
| ▼ What is the simplest form of a fraction? |
| ▼ How do I convert a fraction to a decimal? |
| ▼ How can I add fractions with different denominators? |
| ▼ What is the reciprocal of a fraction? |
| ▼ How do I convert a decimal to a fraction? |
| ▼ Can fractions be negative? |
🔹 References & Sources
The following sources were used to verify the information and formulas presented on this page:
| Source | Type | Link |
|---|---|---|
| Khan Academy - Fractions | Educational Resource | khanacademy.org |
| Math is Fun - Fractions | Educational Guide | mathsisfun.com |
| CK-12 - Converting Decimals to Fractions | Educational Lesson | ck12.org |
| Wikipedia - Fraction (Mathematics) | General Reference | wikipedia.org |