Fraction Calculator
Fraction arithmetic follows different rules depending on the operation. Addition and subtraction require a common denominator, the standard approach is finding the Lowest Common Multiple (LCM) of both denominators, converting each fraction, then adding or subtracting the numerators. Multiplication is simpler: multiply numerators together and denominators together, then simplify. Division is multiplication in disguise, flip the second fraction (take its reciprocal) then multiply. All results should be simplified by dividing both numerator and denominator by their Greatest Common Divisor (GCD). In the Australian school curriculum (F–10), fractions are taught from Year 3 onwards, with operations on fractions a core Year 5–7 topic. This calculator shows step-by-step working for all four operations, add, subtract, multiply, divide, and displays the result as a simplified fraction, a decimal equivalent, and a mixed number simultaneously, making it useful for checking homework, scaling recipes, and construction measurements.
Working
Fill in both fractions above.
Quick: ½=0.5 · ¼=0.25 · ¾=0.75 · ⅓≈0.333 · ⅔≈0.667 · ⅛=0.125
Frequently Asked Questions
How do you add fractions step by step?
To add fractions, first find a common denominator - preferably the least common multiple (LCM) of both denominators, though any common denominator works. Convert each fraction by dividing the LCD by the original denominator and multiplying the result by the original numerator. Add the converted numerators while keeping the denominator the same. Finally, simplify the result if possible. For example, 1/4 + 1/6: LCD is 12, so 3/12 + 2/12 = 5/12. This calculator shows the full working with each step.
How do you multiply fractions?
Multiply fractions by multiplying all numerators together for the new numerator, and all denominators together for the new denominator. No common denominator is needed - this is what makes multiplication simpler than addition. For example, 2/3 x 4/5 = (2 x 4)/(3 x 5) = 8/15. Then simplify by dividing both numerator and denominator by their greatest common divisor. For mixed numbers, convert to improper fractions first before multiplying.
How do you divide fractions?
Divide fractions by flipping the second fraction (finding its reciprocal) and then multiplying. So a/b divided by c/d becomes a/b x d/c. For example, 1/2 divided by 3/4 = 1/2 x 4/3 = 4/6 = 2/3 after simplifying. The reason this works is mathematically sound: dividing by a fraction is the same as multiplying by how many times that fraction fits into 1. The calculator shows each step of this process clearly.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, written as 2 1/3 (two and one-third). It's an alternative representation of an improper fraction where the numerator is larger than the denominator (like 7/3). To convert an improper fraction to a mixed number: divide the numerator by the denominator - the quotient is the whole number and the remainder over the original denominator gives the fraction part. So 7/3 = 2 remainder 1 = 2 1/3. The calculator shows both forms.
How do you simplify a fraction?
Simplify a fraction by finding the greatest common divisor (GCD) of the numerator and denominator, then dividing both by that number. The GCD is the largest number that divides evenly into both. For example, to simplify 12/18: the GCD of 12 and 18 is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2/3. A fraction is in simplest form when no larger number divides both the numerator and denominator. You can find the GCD by listing factors or using the Euclidean algorithm.
Can I convert fractions to decimals?
Yes - simply divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions convert to repeating decimals: 1/3 = 0.333... where the 3 repeats infinitely, and 2/3 = 0.666... The calculator displays all three forms simultaneously: the result as a simplified fraction, the decimal equivalent (truncated to a reasonable number of places for repeating decimals), and the mixed number form, so you can see how they all relate to each other.