maths.free › Arithmetic › Fractions
Fractions
Adding, subtracting, multiplying and dividing fractions with a common denominator.
Fractions add only when they speak the same language, a common denominator. To add ½ and ⅓, rewrite both over 6 (the least common multiple of 2 and 3), add the numerators, and reduce. Multiplication is easier: multiply straight across. Division flips the second fraction and multiplies.
Worked example · 1/2 + 1/3
Step by step
- \frac{1}{3} + \frac{1}{2} = \frac{2}{6} + \frac{3}{6}
Rewrite every fraction over the common denominator 6.
- \frac{2}{6} + \frac{3}{6} = \frac{5}{6}
Add: 2/6 + 3/6 = 5/6.
Reveal the answer
Now you Pick a problem, or type or draw your own. Every step, a picture, the answer hidden until you ask.
Symbols used here
Tap any symbol for the full definition, a picture, and what every letter in it means.
How to: Fractions
- Rewrite every fraction over the common denominator 6.
- Add: 2/6 + 3/6 = 5/6.
Questions people ask
Why does the order of operations matter?
Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.
How do I check an arithmetic answer?
Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.
Why are fractions harder than decimals?
They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.