How do you add or subtract fractions?
Bring both fractions to a common denominator, then add or subtract the numerators: a/b ± c/d = (a×d ± c×b) / (b×d), then simplify. Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6. Using the least common denominator keeps numbers smaller, but any common denominator works — the final simplification gives the same answer.
How do you multiply and divide fractions?
Multiplying is direct: a/b × c/d = (a×c)/(b×d) — multiply numerators together and denominators together. Dividing means multiplying by the reciprocal (invert and multiply): a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
How do you simplify a fraction?
Divide numerator and denominator by their greatest common divisor (GCD). For 10/12, the GCD of 10 and 12 is 2, so 10/12 = 5/6. A fraction is fully simplified (in lowest terms) when the GCD is 1. This calculator simplifies every result automatically and shows the pre-simplified value.
What is a mixed number versus an improper fraction?
An improper fraction has a numerator larger than its denominator (7/4); a mixed number combines a whole number and a proper fraction (1 3/4). Both express the same value. To convert, divide: 7 ÷ 4 = 1 remainder 3 → 1 3/4. This calculator shows both forms plus the decimal.
Why does dividing by a fraction make the answer bigger?
Because division asks how many of the divisor fit into the dividend, and small things fit in more often. Three divided by a quarter is asking how many quarters there are in three, and the answer is twelve. Nothing has been magically created; the question was simply about counting small pieces. Inverting and multiplying is a shortcut for exactly that count. If the reasoning still feels slippery, try it with money: how many 25p coins make three pounds. Once the question is phrased that way, an answer larger than the number you started with stops looking strange.
What is the quickest way to compare two fractions?
Cross-multiply. To compare 7/9 and 5/7, multiply 7 by 7 to get 49 and 5 by 9 to get 45. The larger product sits above the larger fraction, so 7/9 wins. It is the same as finding a common denominator, just without writing the denominator down. For a rough answer even faster, compare each fraction to a familiar benchmark: 7/9 is clearly more than three quarters, 5/7 is a little over two thirds, and that settles it. Both methods beat converting to decimals when the numbers are awkward or when you want to keep exact values.