Simplifying Fractions Calculator

Find the greatest common factor of 36 and 48. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The largest shared factor is 12. Divide both numbers by 12: 36 ÷ 12 = 3 and 48 ÷ 12 = 4. The simplified fraction is 3/4. You can verify it by cross-multiplying: 36 × 4 = 144 and 48 × 3 = 144, so the fractions are equal. A shortcut is to divide by smaller common factors repeatedly — divide 36/48 by 2 to get 18/24, by 2 again to get 9/12, then by 3 to get 3/4. Both methods reach the same answer. If you need to convert that result to a percentage, 3/4 equals 75%, which you can confirm with our percentage calculator.

It means the numerator and denominator have no common factor other than 1, so the fraction cannot be reduced further. For example, 7/9 is already in lowest terms because the factors of 7 are 1 and 7, and the factors of 9 are 1, 3, and 9 — the only shared factor is 1. The calculator will return 7/9 unchanged. This is called a coprime pair. Other examples include 5/8, 11/12, and 13/20. Even large fractions can be in simplest form: 97/100 stays as is because 97 is prime and doesn't divide 100. If you're checking whether a fraction needs simplifying, compare the numerator and denominator to see if both are even (divisible by 2), both end in 0 or 5 (divisible by 5), or both divisible by 3 using the digit-sum rule. If none apply, it's likely already simplified. You can also use our percentage change calculator to compare the decimal values of two fractions quickly.

Write the percentage over 100 first, so 45% becomes 45/100. Then find the greatest common factor of 45 and 100. The factors of 45 are 1, 3, 5, 9, 15, 45, and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The GCF is 5. Divide both by 5: 45 ÷ 5 = 9 and 100 ÷ 5 = 20. The simplified fraction is 9/20. As a decimal, 9/20 equals 0.45, which matches 45%. For percentages with decimals, like 12.5%, multiply the numerator and denominator by 10 first to get 125/1000, then simplify by dividing both by 125 to get 1/8. Remember that percentages over 100, such as 150%, become improper fractions: 150/100 simplifies to 3/2, or 1 1/2 as a mixed number. If you need the reverse — turning a fraction back into a percentage — divide the numerator by the denominator and multiply by 100. Our percentage increase calculator handles those comparisons well.

Simplifying means reducing a fraction to its smallest possible numerator and denominator, while finding an equivalent fraction means creating a larger or different version that has the same value. For example, 2/3 is the simplified form of 8/12. But 16/24 is also equivalent to 2/3 — it's just not simplified. Simplifying always moves toward smaller numbers; finding equivalents can move in either direction. The key rule is that multiplying or dividing both the numerator and denominator by the same non-zero number keeps the value unchanged. So 2/3 × 4/4 = 8/12 and 8/12 ÷ 4/4 = 2/3. In cooking, if a recipe calls for 3/4 cup of flour, that's the same as 6/8 cup or 12/16 cup — all equivalent, but 3/4 is the simplest. When adding fractions with different denominators, you often create equivalent fractions first, then simplify the answer. For instance, 1/4 + 1/6 = 3/12 + 2/12 = 5/12, which is already simplified. Our percentage calculator can help you check these values in decimal form.

Yes. The calculator reduces improper fractions — where the numerator is larger than the denominator — just like proper fractions. For example, 30/45 simplifies to 2/3 because the GCF of 30 and 45 is 15. The fact that the fraction is improper doesn't affect the simplification process. If you have a mixed number like 2 3/4, convert it to an improper fraction first: multiply the whole number by the denominator (2 × 4 = 8), add the numerator (8 + 3 = 11), and place it over the original denominator to get 11/4. The fraction 11/4 is already in lowest terms since the GCF of 11 and 4 is 1. A mixed number like 4 6/8, however, converts to 38/8, which simplifies to 19/4, or 4 3/4. The fractional part simplifies, but the whole number stays the same. If your result is an improper fraction and you want a mixed number, divide the numerator by the denominator: 19 ÷ 4 = 4 with a remainder of 3, so 19/4 = 4 3/4. Use our percentage change calculator to compare improper fractions as decimals.

The most common reason is that your teacher may want a mixed number instead of an improper fraction, or vice versa. If you enter 22/8, the calculator returns 11/4 — a correct simplified improper fraction. Your teacher might expect 2 3/4 as a mixed number. Both are correct; they're just different forms. Another reason is that some teachers require you to show the GCF step-by-step rather than just the final answer. The calculator does the math instantly, but showing your work means listing factors: for 22/8, the factors of 22 are 1, 2, 11, 22, and the factors of 8 are 1, 2, 4, 8, so the GCF is 2, giving 11/4. A third possibility is rounding. If the calculator shows a decimal like 0.6667 for 2/3, that's a rounded value — the exact fraction is 2/3, which repeats forever as 0.666.... Always trust the fraction over the rounded decimal. If your teacher asks for the answer as a percentage, convert 2/3 by dividing 2 by 3 to get 0.6667, then multiply by 100 to get 66.67%. Our percentage calculator can double-check that conversion.