Equivalent Fractions Calculator
Generate a list of equivalent fractions for any given fraction. Shows the simplified form and up to 10 equivalents.
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How to use this calculator
Equivalent fractions are created by multiplying numerator and denominator by the same non-zero integer. They represent the same value on the number line.
- 1
Enter the numerator and denominator of your base fraction.
- 2
Choose how many equivalents to generate (1–10).
- 3
The simplified form is shown first, then equivalents by multiplying by 1, 2, 3, … up to your chosen count.
Frequently asked questions
Why is the first equivalent not the fraction I typed?
The list is built from the simplified fraction, not from your original entry. If you type 6/8, the tool reduces it to 3/4 and then shows × 1 = 3/4, × 2 = 6/8, × 3 = 9/12 and so on. Your own fraction appears further down the list, here at × 2, as long as the count you chose is at least that high.
What does the “Simplified form” line mean?
It is the fraction divided through by the greatest common divisor of numerator and denominator, so 6/8 becomes 3/4 and 9/3 becomes 3/1. A fraction in lowest terms has no whole number greater than 1 that divides both parts, and every fraction has exactly one such form.
How are negative numbers displayed?
The minus sign always ends up on the numerator. Entering 5 over −15 gives −1/3, and −4 over −10 gives 2/5, because two negatives cancel. Every equivalent in the list keeps that sign, for example −1/3, −2/6, −3/9.
What happens when the numerator is zero?
Zero over any non-zero denominator reduces to 0/1, and the equivalents are 0/2, 0/3 and so on, all with a decimal value of 0. A zero denominator is rejected with an error because division by zero is undefined.
Can I enter decimals such as 2.5/4?
No. Both numerator and denominator must be whole numbers, and decimals return an error instead of being rounded. To use 2.5/4, multiply top and bottom by 2 first and enter 5 and 8, which gives the simplified form 5/8.
How many equivalents can I list?
Between 1 and 10. A larger number is capped at 10 and a smaller one, including 0, which is also what a cleared box becomes, raised to 1. The multipliers are always 1, 2, 3 and so on in order, so the tool cannot be told to skip to, say, a denominator of 100.
How do I find the equivalent fraction with a specific denominator?
Divide the target denominator by the simplified denominator. It works only when the result is a whole number. For 3/4 and a target of 20, 20 ÷ 4 = 5, which matches the × 5 line, 15/20. A target of 18 gives no whole multiplier because 18 ÷ 4 is 4.5, so no equivalent of 3/4 has a denominator of 18.
Equivalent fractions and simplest form
Same value, different numbers
Two fractions are equivalent when they name the same point on the number line. Multiplying or dividing the numerator and denominator by the same non-zero whole number leaves the value untouched, so 1/3, 2/6 and 3/9 are all one third. The calculator reduces your fraction to lowest terms with the greatest common divisor, lists its first few multiples, and prints the decimal value at the end.
| Multiplier | Fraction | Multiplier | Fraction |
|---|---|---|---|
| × 1 | 3/4 | × 6 | 18/24 |
| × 2 | 6/8 | × 7 | 21/28 |
| × 3 | 9/12 | × 8 | 24/32 |
| × 4 | 12/16 | × 9 | 27/36 |
| × 5 | 15/20 | × 10 | 30/40 |
Worked example: a fraction that is not in lowest terms
Typing 6 over 8 with a count of 4 gives a simplified form of 3/4, then 3/4, 6/8, 9/12 and 12/16, and a decimal value of 0.75. The greatest common divisor of 6 and 8 is 2, so dividing both by 2 produced 3/4. In the other direction, 9 over 3 reduces to 3/1, a whole number, and its equivalents are 6/2 and 9/3.
Worked example: a common denominator task
To add 1/3 and 3/4 you want equal denominators. The default input of 1/3 lists 2/6, 3/9, 4/12 and 5/15, and 3/4 lists 6/8, 9/12, 12/16, so both have a fraction with denominator 12: 4/12 and 9/12. Their sum is 13/12. Scanning the two lists for a shared denominator is a hands-on way to find a common denominator, and the first match is the least one here.
Checking equivalence by cross-multiplying
To test whether a/b equals c/d, compare a × d with b × c. For 6/8 and 9/12, both products equal 72, so they are equivalent. Another test is to reduce both fractions: if their simplified forms are identical, they match. The tool does the second test for any fraction you enter, since 6/8 and 9/12 both reduce to 3/4.
Input rules
Numerator and denominator must be whole numbers, the denominator cannot be zero, and the list length is limited to 10 multiples. Signs are normalised so the denominator is positive. Decimal values are shown to at most eight places with trailing zeros removed, which is why 1/3 appears as 0.33333333 rather than an exact repeating decimal.
Learn more from an authoritative source:
WikipediaLCD — Least Common Denominator
Find the Least Common Denominator (LCD) of up to four denominators, with prime factorization method shown step-by-step.
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