Add, subtract, multiply, divide, and simplify fractions. Convert between fractions and decimals.
Choose the operation you want to perform: Add, Subtract, Multiply, Divide, Simplify, or Convert between fractions and decimals.
Input the numerator and denominator for your fraction(s). For operations with two fractions, enter both sets of values.
Press the Calculate button to process your fraction operation.
Your result will display in fraction form, mixed number form (if applicable), and decimal form. Results are automatically simplified.
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 38, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. If a person were to eat 3 slices, the remaining fraction of the pie would be 58.
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 addition, subtraction, multiplication, division, and simplification.
Unlike adding integers such as 2 and 8, fractions require a common denominator to undergo addition. One method for finding a common denominator involves multiplying the numerators and denominators of all fractions involved by the product of the denominators of each fraction.
Formula:
ab + cd = (a×d + c×b)(b×d)
Example: 34 + 16 = (3×6 + 1×4)(4×6) = 2224 = 1112
An alternative method is to find the least common multiple (LCM) of the denominators, which is often more efficient and results in a fraction closer to simplified form.
Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. The process is identical to addition, except you subtract the numerators instead of adding them.
Formula:
ab - cd = (a×d - c×b)(b×d)
Example: 34 - 16 = (3×6 - 1×4)(4×6) = 1424 = 712
Multiplying fractions is straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator. Simply multiply the numerators together and the denominators together to get your result.
Formula:
ab × cd = (a×c)(b×d)
Example: 34 × 16 = 324 = 18
If possible, the solution should be simplified by dividing both numerator and denominator by their greatest common factor.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and denominator.
Formula:
ab ÷ cd = ab × dc = (a×d)(b×c)
Example: 34 ÷ 16 = 34 × 61 = 184 = 92
Simplifying fractions makes them easier to work with. A fraction is simplified by dividing both the numerator and denominator by their greatest common factor (GCD), resulting in an equivalent fraction in its lowest terms.
Example:
220440 = 1120 (both divided by 20)
The calculator automatically returns fraction results in both improper fraction form and mixed number form, with both presented in their lowest terms.
Converting from decimals to fractions requires understanding that each decimal place represents a power of 10. For example, the number 0.1234 has 4 decimal places, representing 10^4 (10,000). This makes the fraction 123410000, which simplifies to 6175000.
Converting fractions to decimals can be done through long division. For fractions with denominators that are powers of 10, you can simply move the decimal point.
Example: 12 = 510 = 0.5
Example: 34 = 75100 = 0.75
Perfect for students learning fraction arithmetic and operations
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Verify answers and understand how fraction operations work
A fraction is a number that represents part of a whole. It consists of a numerator (top number) and a denominator (bottom number). The numerator shows how many parts you have, while the denominator shows how many equal parts the whole is divided into.
The Greatest Common Divisor (GCD) is the largest number that divides evenly into both the numerator and denominator. We use it to simplify fractions by dividing both numbers by their GCD, reducing the fraction to its simplest form.
To add fractions, you need a common denominator. Find the least common multiple of both denominators, convert each fraction to use this common denominator, then add the numerators while keeping the denominator the same.
A mixed number combines a whole number with a fraction, like 2 3/4. It represents the same value as an improper fraction (where the numerator is larger than the denominator), just in a different form.
Count the number of decimal places. Use a power of 10 as the denominator (10 for one decimal place, 100 for two, etc.) and put the decimal digits as the numerator. Then simplify the resulting fraction.
Yes! To divide by a fraction, multiply by its reciprocal (flip the numerator and denominator). For example, 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4 = 3/2.
Simplifying means reducing a fraction to its lowest terms. This is done by dividing both the numerator and denominator by their greatest common factor, resulting in an equivalent fraction that's easier to understand.
If you enter operations that result in a negative denominator, the calculator automatically converts it so the denominator is positive, placing the negative sign on the numerator instead.
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