AI Fractions Solver

The four rules for fraction arithmetic

• Add or subtract: make the denominators the same, then add or subtract the numerators only.
• Multiply: multiply numerators together and denominators together.
• Divide: flip the second fraction (take its reciprocal) and multiply.
• Simplify: divide the top and bottom by their greatest common factor.

The denominator is the size of the pieces and the numerator is how many you have, which is why you can only add pieces that are the same size.

Mixed numbers and improper fractions

A mixed number such as 1 7/12 is a whole number plus a fraction. To calculate with it, convert it to an improper fraction first: 1 7/12 = (1 × 12 + 7)/12 = 19/12. After the calculation, convert back by dividing the numerator by the denominator and writing the remainder over the denominator.

Fractions inside algebra

The same rules apply to algebraic fractions, which is why fraction fluency matters later. Equations with fractions can be cleared by multiplying through, as shown in the linear equation solver. For a slower walkthrough of the most common operation, read how to add fractions.

Worked examples

Example 1: Add 3/4 + 5/6

1. The lowest common denominator of 4 and 6 is 12.
2. Convert: 3/4 = 9/12 and 5/6 = 10/12.
3. Add the numerators: 9 + 10 = 19, giving 19/12.
4. As a mixed number, 19/12 = 1 7/12.

Final answer: 19/12 = 1 7/12 ≈ 1.583

Example 2: Subtract 5/8 − 1/3

1. The lowest common denominator is 24.
2. Convert: 5/8 = 15/24 and 1/3 = 8/24.
3. Subtract: 15 − 8 = 7.

Final answer: 7/24

Example 3: Multiply 2/3 × 9/10

1. Multiply the numerators: 2 × 9 = 18.
2. Multiply the denominators: 3 × 10 = 30.
3. Simplify 18/30 by dividing by 6.

Final answer: 3/5

Example 4: Divide 3/5 ÷ 9/10

1. Flip the second fraction and multiply: 3/5 × 10/9.
2. Multiply: 30/45.
3. Divide top and bottom by 15.

Final answer: 2/3

Common mistakes to avoid

• Adding the denominators as well as the numerators: 1/2 + 1/3 is not 2/5.
• Flipping the wrong fraction when dividing; only the second one is inverted.
• Forgetting to reduce the answer to lowest terms.
• Multiplying the whole number of a mixed number by the fraction instead of converting first.
• Using a common denominator that works but is far larger than needed, which makes simplifying harder.

Frequently asked questions

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