{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"fraction-arithmetic"},"result":{"entity_type":"calculator","id":"fraction-arithmetic","calculator_id":"fraction-arithmetic","canonical_url":"https://tttkmbb.com/math/fraction-arithmetic","name":"Fraction Calculator","title":"Fraction Calculator – Add, Subtract, Multiply and Divide Fractions and Mixed Numbers Exactly","category":"math","category_name":"Math","tool_name":"calculate_fraction_arithmetic","featured_mcp_tool":true,"description":"Adds, subtracts, multiplies or divides two fractions, mixed numbers, whole numbers or decimals with exact integer arithmetic, returning the result in lowest terms, as a mixed number and as a decimal, with the intermediate steps.","use_when":"You need an exact result of an operation on two fractions (e.g. 3/4 + 1/6), including mixed numbers such as 1 1/2, rather than a rounded decimal.","do_not_use_when":"You only want to reduce a single fraction or convert it to a decimal or percent (use fraction-simplifier), or you need the least common denominator of several denominators (use gcd-lcm).","inputs":[{"name":"fraction_a","label":"First fraction","type":"string","required":true,"description":"First operand: a fraction '3/4', a mixed number '1 1/2' or '-1 1/2', a whole number '5' or a decimal '0.75'.","example":"3/4"},{"name":"fraction_b","label":"Second fraction","type":"string","required":true,"description":"Second operand in the same formats.","example":"1/6"},{"name":"operation","label":"Operation","type":"enum","required":false,"default":"add","values":[{"value":"add","label":"Add (+)","aliases":["+","plus","sum","addition"]},{"value":"subtract","label":"Subtract (−)","aliases":["-","minus","difference","subtraction"]},{"value":"multiply","label":"Multiply (×)","aliases":["*","x","times","product","multiplication"]},{"value":"divide","label":"Divide (÷)","aliases":["/","over","quotient","division"]}],"description":"Operation applied as fraction_a (operation) fraction_b.","example":"add"}],"outputs":[{"name":"result","label":"Result","type":"string","decimals":4,"description":"Exact result in lowest terms with the sign in the numerator, e.g. '11/12' (a whole number when the denominator reduces to 1)."},{"name":"mixed_number","label":"Mixed number","type":"string","decimals":4,"description":"Result as whole part plus proper fraction, e.g. '1 1/2'."},{"name":"numerator","label":"Numerator","type":"integer","decimals":0,"description":"Numerator of the reduced result."},{"name":"denominator","label":"Denominator","type":"integer","decimals":0,"description":"Denominator of the reduced result (always positive)."},{"name":"decimal","label":"Decimal","type":"number","decimals":6,"description":"numerator / denominator."},{"name":"working","label":"Working","type":"string","decimals":4,"description":"Steps: operands in lowest terms, the common-denominator or reciprocal step, the unreduced result and the reduced result."}],"input_schema":{"type":"object","properties":{"fraction_a":{"description":"First operand: a fraction '3/4', a mixed number '1 1/2' or '-1 1/2', a whole number '5' or a decimal '0.75'.","type":"string","examples":["3/4"]},"fraction_b":{"description":"Second operand in the same formats.","type":"string","examples":["1/6"]},"operation":{"description":"Operation applied as fraction_a (operation) fraction_b.","type":"string","enum":["add","subtract","multiply","divide"],"default":"add","examples":["add"]}},"additionalProperties":false,"required":["fraction_a","fraction_b"]},"output_schema":{"type":"object","properties":{"result":{"description":"Exact result in lowest terms with the sign in the numerator, e.g. '11/12' (a whole number when the denominator reduces to 1).","type":"string"},"mixed_number":{"description":"Result as whole part plus proper fraction, e.g. '1 1/2'.","type":"string"},"numerator":{"description":"Numerator of the reduced result.","type":"integer"},"denominator":{"description":"Denominator of the reduced result (always positive).","type":"integer"},"decimal":{"description":"numerator / denominator.","type":"number"},"working":{"description":"Steps: operands in lowest terms, the common-denominator or reciprocal step, the unreduced result and the reduced result.","type":"string"}}},"formula":"a/b + c/d = (a·(L/b) + c·(L/d)) / L with L = lcm(b, d), a/b − c/d likewise; a/b × c/d = (a·c) / (b·d); a/b ÷ c/d = (a·d) / (b·c); the result is divided by gcd(numerator, denominator)","method":"Operands are parsed to exact integer numerators and denominators (a decimal becomes k/10^n) and combined with arbitrary-precision integers, so the fraction outputs are exact for any input size; only the decimal output is rounded.","sources":[{"name":"Wikipedia – Fraction – arithmetic with fractions","url":"https://en.wikipedia.org/wiki/Fraction#Arithmetic_with_fractions","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Lowest common denominator","url":"https://en.wikipedia.org/wiki/Lowest_common_denominator","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wolfram MathWorld – Fraction","url":"https://mathworld.wolfram.com/Fraction.html","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"3/4 + 1/6","inputs":{"fraction_a":"3/4","fraction_b":"1/6","operation":"add"},"expected":{"result":"11/12","mixed_number":"11/12","numerator":11,"denominator":12,"decimal":0.916667,"working":"3/4 + 1/6 = 9/12 + 2/12 = 11/12"},"url":"https://tttkmbb.com/api/v1/calculate/fraction-arithmetic?fraction_a=3%2F4&fraction_b=1%2F6&operation=add"},{"name":"2 1/3 − 5/6","inputs":{"fraction_a":"2 1/3","fraction_b":"5/6","operation":"subtract"},"expected":{"result":"3/2","mixed_number":"1 1/2","numerator":3,"denominator":2,"decimal":1.5,"working":"7/3 − 5/6 = 14/6 − 5/6 = 9/6 = 3/2"},"url":"https://tttkmbb.com/api/v1/calculate/fraction-arithmetic?fraction_a=2+1%2F3&fraction_b=5%2F6&operation=subtract"}],"faq":[{"q":"How do I enter a negative mixed number?","a":"Put the sign in front of the whole part: '-1 1/2' means −(1 + 1/2) = −3/2. A sign on the numerator or denominator of a plain fraction ('-3/4' or '3/-4') is also accepted."},{"q":"Can I enter decimals?","a":"Yes. A decimal such as 0.75 is converted exactly to 75/100 = 3/4 before the operation, so 0.75 + 1/6 gives 11/12."},{"q":"Why is the working shown with a common denominator?","a":"Addition and subtraction use the least common denominator L = lcm(b, d), e.g. 3/4 + 1/6 = 9/12 + 2/12; multiplication and division do not need one."}],"tags":["fraction calculator","add fractions","subtract fractions","multiply fractions","divide fractions","mixed numbers"],"related":[{"calculator_id":"fraction-simplifier","reason":"Reduce a single fraction or convert it to decimal and percent."},{"calculator_id":"gcd-lcm","reason":"The LCM used as common denominator and the GCD used to reduce."},{"calculator_id":"ratio","reason":"Simplify a ratio a:b, including decimal terms."}],"links":{"html":"https://tttkmbb.com/math/fraction-arithmetic","markdown":"https://tttkmbb.com/math/fraction-arithmetic.md","json":"https://tttkmbb.com/math/fraction-arithmetic.json","api":"https://tttkmbb.com/api/v1/calculate/fraction-arithmetic","schema":"https://tttkmbb.com/api/v1/calculators/fraction-arithmetic","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:51:38Z","next_actions":[{"tool":"calculate_fraction_arithmetic","calculator_id":"fraction-arithmetic","reason":"Run Fraction Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/math/fraction-arithmetic.md"}}