VITON13 SCHOOL · Maths
Fraction calculator with steps
Fractions, mixed numbers and whole numbers with + − × ÷ — the answer as a fraction, a mixed number, a decimal and a percent, with every step written out.
Leave the whole part empty for a simple fraction, or fill in only the whole part for a whole number. A minus sign is allowed.
94
- Fraction
- 94
- Mixed number
- 214
- Decimal
- 2.25
- Percent
- 225%
Step by step
- Turn the mixed number into an improper fraction112=1 × 2 + 12=32
- Find the lowest common denominatorLCM(2, 4)=4
- Rewrite the fractions over the common denominator32=3 × 22 × 2=6434
- Add the numerators64+34=6 + 34=94
- Write the answer as a mixed number94=9 ÷ 4=214
Picture
- 32
- 34
- Answer94
How to use the fraction calculator
- Enter the fractionsUp to four numbers — a whole number, a fraction or a mixed number (whole part, numerator, denominator) — with + − × ÷ between them. Or type the whole expression.
- Read the answer in four formsThe result is a simplified fraction, a mixed number, a decimal with the repeating part in brackets and a percent, updated as you type.
- Follow the steps and the pictureEach step is one line of maths: mixed numbers converted, the common denominator, the reciprocal, simplifying by the GCD. Bars or circles show the sizes.
Exact arithmetic, not rounded decimals
The calculator keeps every number as a numerator and a denominator made of whole numbers of any length, and never rounds along the way. That is why 1/3 + 1/3 + 1/3 comes out as exactly 1, and why the decimal it shows is worked out by long division from the exact fraction.
Multiplication and division are done before addition and subtraction, and brackets come first, as in written maths. In the expression mode a fraction typed with whole numbers, such as 1/2, is read as one number, and a whole number followed by a space and a fraction, such as 1 1/2, is a mixed number.
Three more modes help with homework: simplify a fraction with Euclid's algorithm written out, compare two fractions over a common denominator, and turn a decimal into a fraction — exactly for a terminating decimal or one with the repeating part in brackets.
Questions about fractions
How do you add fractions with different denominators?
Find the lowest common denominator (the LCM of the denominators), rewrite each fraction over it, add the numerators and simplify. For 1/4 + 1/6: LCM(4, 6) = 12, so 3/12 + 2/12 = 5/12.
How do you divide fractions?
Multiply by the reciprocal of the second fraction: flip it and multiply. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. Division by zero has no value, so the calculator stops and says so.
How does the calculator read 1 1/2 + 3/4 × 2/5?
1 1/2 is a mixed number, and multiplication goes before addition: 3/4 × 2/5 = 3/10, then 3/2 + 3/10 = 18/10 = 9/5 = 1 4/5. A fraction typed with whole numbers is one number, so 3 ÷ 1/2 = 6.
Why are some decimals shown with brackets?
Some fractions never end as decimals: 1/3 = 0.333… The repeating digits are put in brackets, so 1/3 = 0.(3) and 1/6 = 0.1(6). When the repeating block is very long, the decimal is cut at 60 places and ends with an ellipsis.
Related guides
- How to add fractions: same and different denominators, mixed numbers and simplifyingHow to add fractions with the same or different denominators, add mixed numbers, subtract, and simplify the answer with the GCD. Worked examples.
- How to divide fractions: keep, change, flip, and why it worksHow to divide fractions by multiplying by the reciprocal, why it works, plus multiplying fractions, mixed numbers and whole numbers, with examples.
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