The formula this page uses
a/b in lowest terms = (a ÷ g) / (b ÷ g), where g = GCF(a, b). It is finished when GCF(top, bottom) = 1.
Reduce any fraction to its simplest form
Use the free simplify fractions calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Arithmetic
Simplify Fractions Calculator explained
The short version
- A fraction is in lowest terms when the top and bottom share no factor except 1.
- Dividing both by the same number never changes the value, only how it looks.
- You can chip away with small factors, or divide once by the greatest common factor and finish immediately.
What each part means
SymbolWhat it means
a — NumeratorThe top number. It can be bigger than the bottom without changing anything here.
b — DenominatorThe bottom number. It can never be 0.
g — Greatest common factorThe biggest number dividing both. Dividing by it finishes the job in one move.
lowest terms — The finished fractionAlso called simplest form. It is the version every marker expects.
Show your work: a full example
- Simplify 84/12684/126
- Both are even, so divide by 284 ÷ 2 = 42 and 126 ÷ 2 = 63, giving 42/63
- Both digit-sums are multiples of 3, so divide by 342 ÷ 3 = 14 and 63 ÷ 3 = 21, giving 14/21
- Both are in the 7 times table14 ÷ 7 = 2 and 21 ÷ 7 = 3, giving 2/3
- 2 and 3 share nothing, so stop84/126 = 2/3
- The one-step versionGCF(84, 126) = 42, and 84 ÷ 42 = 2 with 126 ÷ 42 = 3
A second, different case
- A different case: no even numbers anywhere91/117
- 2 is no helpboth numbers are odd
- Test 3 with digit sums9 + 1 = 10, not a multiple of 3, so 3 is out
- Test 791 ÷ 7 = 13, but 117 ÷ 7 leaves a remainder
- Test 1391 ÷ 13 = 7 and 117 ÷ 13 = 9
- Write the answer91/117 = 7/9
- Compare with one that will not budge8/15, since 8 = 2 × 2 × 2 and 15 = 3 × 5 share no prime
Copy-ready example
84/126
Simplify 84/126
Questions about the Simplify Fractions Calculator
How do I know for certain that I have finished?
Check whether any prime divides both numbers. In practice you only have to try 2, 3, 5, 7, 11 and 13 for the fractions in school work. If none of them divides both, the fraction is in lowest terms and you can stop looking.
What quick tests help me spot a shared factor?
Both even means 2 works. Both digit-sums being multiples of 3 means 3 works. Both ending in 0 or 5 means 5 works. After that, try 7, 11 and 13 by dividing directly, since there is no shortcut worth memorising for them.
Do I always have to simplify my answer?
Most markers expect it, and it makes answers easier to compare, since 2/3 and 84/126 look nothing alike until one is reduced. The exception is when the question sets a fixed bottom number, such as asking for the answer in twelfths.
What if there is a decimal in my fraction, like 0.6/0.8?
Multiply the top and the bottom by the same power of ten until both are whole numbers. Here multiplying by 10 gives 6/8, which reduces to 3/4. It is the same value all along, since multiplying both parts by 10 is multiplying by 1.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.
GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.