Fraction Calculator
Exact fraction answers with the working shown — LCD, cross-cancelling and all.
Answer
This is the last answer worked out. Fix the calculation above to update it.
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Working
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| # | Number | Fraction | Over the LCD | Decimal |
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Working
About the Fraction Calculator
Type a calculation the way you would write it on paper — 1 1/2 + 3/4 × 2/5, 84/126 or (2/3)^2 ÷ 1 1/8 — and get the exact answer as a simplified fraction, a mixed number and a decimal, with repeating digits marked.
Every operation is shown step by step: mixed numbers turned into improper fractions, the lowest common denominator for adding and subtracting, cross-cancelling before multiplying, and multiplying by the reciprocal to divide. The arithmetic uses whole-number fractions of any size, so there is no rounding until the final decimal. A second mode puts a list of fractions, decimals and mixed numbers in order.
How to use it
- Type your calculation. Write fractions as
3/4, mixed numbers as1 1/2(a space between the whole number and the fraction), and use + − × ÷,^for powers and brackets.*,xand:work too. - Check You entered to see how your input was read, with each fraction stacked.
- Read the answer as a fraction, a mixed number and a decimal. The Working list explains each step; Copy working copies it as text.
- To compare or order fractions, switch to Compare & order, type them separated by commas and choose smallest or largest first.
Examples
1 1/2 + 3/4 × 2/5
9/5 = 1 4/5 = 1.8
The multiplication comes first: 3/4 × 2/5 = 3/10 (cancel the 2 and the 4 first). Then 3/2 + 3/10 = 15/10 + 3/10 = 18/10 = 9/5.
1/2 ÷ 3/4
2/3
Dividing by 3/4 is the same as multiplying by 4/3: 1/2 × 4/3 = 4/6 = 2/3.
84/126
2/3
The greatest common factor of 84 and 126 is 42; 84 ÷ 42 = 2 and 126 ÷ 42 = 3.
5/6 − 1/2
1/3 = 0.333… (shown with a bar over the repeating 3)
5/6 − 3/6 = 2/6, which simplifies to 1/3.
3/4, 5/7, 2/3
2/3 < 5/7 < 3/4
Over the common denominator 84 they are 56/84, 60/84 and 63/84.
Common uses
- Checking homework and seeing the method for each step.
- Adding up measurements in inches and fractions of an inch.
- Scaling recipe quantities such as 2/3 cup × 1 1/2.
- Putting fractions and decimals in order from smallest to largest.
The rules it follows
- Adding or subtracting: rewrite both fractions over the lowest common denominator (the LCM of the denominators), then add or subtract the numerators.
- Multiplying: multiply the numerators and the denominators. Cancelling common factors across the fractions first keeps the numbers small.
- Dividing: multiply by the reciprocal of the second fraction (turn it upside down).
- Powers: raise the numerator and the denominator to the power; a negative power means the reciprocal.
- Simplifying: divide the numerator and the denominator by their greatest common factor, found with Euclid’s algorithm.
- Order of operations: brackets, then powers, then × and ÷ from left to right, then + and − from left to right.
How the input is read
A slash between two numbers makes one fraction, so 1/2 ÷ 3/4 is (1/2) ÷ (3/4), the way it looks on paper. A whole number followed by a space and a fraction is a mixed number: 2 3/4 means 2 + 3/4, and -1 1/2 means −(1 + 1/2) = −3/2. A slash after a bracket divides, so (1/2)/(3/4) also gives 2/3. Decimals are converted exactly: 0.75 becomes 75/100 = 3/4.
When does a fraction have a repeating decimal?
A fraction in lowest terms has a terminating decimal only when its denominator has no prime factors other than 2 and 5. So 3/8 = 0.375 ends, while 1/6 = 0.1666… repeats because 6 = 2 × 3. The answer draws a line over the repeating block (for 1/6, over the 6). It is found by long division: when a remainder comes back, the digits repeat from there.
Limitations
- Powers must be whole numbers, or simple roots (such as 1/2 or 1/3) that give an exact fraction: (4/9)^(1/2) = 2/3 works, but 2^(1/2) is irrational, so use the scientific calculator for it.
- Numbers can have up to 40 digits and answers up to 2,000 digits.
- There are no variables, so algebraic fractions such as x/2 + x/3 are not supported.
- The fraction model is drawn for denominators up to 24 and values up to 10.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How do I add fractions with different denominators?
Find the lowest common denominator — the smallest number both denominators divide into — and rewrite each fraction over it. For 1/4 + 1/6 the LCD is 12, so 1/4 = 3/12 and 1/6 = 2/12, and the sum is 5/12. The calculator shows this rewriting for every addition and subtraction.
How do I divide fractions?
Multiply the first fraction by the reciprocal of the second: a/b ÷ c/d = a/b × d/c. For example 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
How do I enter a mixed number?
Type the whole number, a space, then the fraction: 2 3/4. For a negative mixed number put the minus in front: -2 3/4 means −2 3/4 = −11/4. Characters such as ½ and ¾ are understood too.
What is the difference between an improper fraction and a mixed number?
An improper fraction has a numerator at least as big as its denominator, such as 9/5. The same value as a mixed number is 1 4/5: one whole and four fifths. The calculator shows both, and the decimal 1.8.
How do I compare two fractions?
Cross-multiply: for 3/4 and 5/7, compare 3 × 7 = 21 with 5 × 4 = 20. Since 21 > 20, 3/4 is larger. With more than two fractions, rewrite them all over a common denominator and compare the numerators — Compare & order does both.
Why does 6/2(1+2) give 9?
Here 6/2 is read as one fraction (3), which is then multiplied by (1 + 2), giving 9. If you mean 6 divided by 2(1 + 2), add brackets: 6/(2(1+2)) gives 1.