How to solve it
- Solve what is inside parentheses first.
- Then solve the powers.
- Solve multiplications and divisions from left to right.
- Finally, additions and subtractions from left to right.
2/3 + 1/2 × 3/4
1/2 × 3/4 = 3/8
2/3 + 3/8 = 16/24 + 9/24 = 25/24
Result: 25/24
Common mistake:Wrong: 1/2 + 1/3 × 3/4 = 5/6 × 3/4 = 5/8.Right: 1/2 + 1/3 × 3/4 = 1/2 + 1/4 = 3/4.Adding from left to right ignores that multiplication comes first. Compute 1/3 × 3/4 = 1/4 first.
For a single operation between two fractions, use the fraction operations index; this page decides the order inside a calculation with several.
Worked example: 1/2 + 3/4 × 2/3
The expression mixes an addition and a product, with no parentheses. What is calculated first, and what is the value?
- Find the product. Multiplication has higher priority than addition, so it is done first. Then 3/4 × 2/3 = 6/12 = 1/2.
- Substitute and add. The expression becomes 1/2 + 1/2 = 2/2 = 1.
Final result: 1.
Check. With decimals, 3/4 × 2/3 ≈ 0.75 × 0.667 = 0.50025 (0.667 − 2/3 = 1/3000, an error on the high side), close to 0.5; 0.5 + 0.5 = 1.
The calculator shows one line for each operation it performs. Here there are three (the product on two lines, because of the way it reads the bar, and the sum), since fractions that are already written do not count as a calculation.
The four levels of the order of operations
The order of operations ranks operations in levels. Within the level of × and ÷, and within the level of + and −, you go from left to right; parentheses or brackets lift their contents to the first level.
| Level | Expression | Result |
|---|---|---|
| 1. Parentheses and brackets | (1/2 + 3/4) × 2/3 | 5/6 |
| 2. Powers | 3 × (1/3)^-2 = 3 × 9 | 27 |
| 3. × and ÷ from left to right | 3/5 ÷ 3/10 × 2 = 2 × 2 | 4 |
| 3. If you group the product | 3/5 ÷ (3/10 × 2) = 3/5 ÷ 3/5 | 1 |
| 4. + and − from left to right | 9/10 − 2/5 + 1/10 = 5/10 + 1/10 | 3/5 |
| 4. If you group the sum | 9/10 − (2/5 + 1/10) = 9/10 − 5/10 | 2/5 |
The paired rows show that a parenthesis changes the value even though the numbers are the same. Left to right has a reason: dividing by 3/10 is multiplying by 10/3, so the level 3 row equals 3/5 × 10/3 × 2 = 4. Grouping the product after the division changes the divisor, and with it the result. Subtraction works in a similar way: subtracting a term is the same as adding its opposite, which is why 8 − 3 + 2 reads as 8 + (−3) + 2.
Signs, powers and bars
The minus sign and the fraction bar are the two places where a reading goes astray. In math notation, a sign in front of a power is not part of the base, so −3² = −(3²) = −9. In spreadsheets and some programs the sign is included in the number and the result would be 9. The calculator follows math notation.
| You type | Reading | Result |
|---|---|---|
| -3^2 | −(3^2) | −9 |
| (-3)^2 | (−3) × (−3) | 9 |
| 2^3^2 | 2^(3^2) = 2^9 | 512 |
| 1/3/1/5*2 | chain of divisions from left to right | 2/15 |
| (1/3)/(1/5)*2 | (1/3 ÷ 1/5) × 2 | 10/3 |
Stacked powers group from the top, a^(b^c), which is the usual convention; with the ^ symbol there is no universal agreement, and 4^3^2 gives different results depending on the program. With ÷ between fractions, each one is read as a whole, and with the bar alone the divisions chain together. If an expression allows two readings, parentheses separate them at no cost.
Each expression can have up to 1024 characters; going over gives an error, never a partial result.
Which calculator to use for which calculation
For a single operation between two fractions, the fraction calculator and the page for each operation explain the method in more detail. If the expression is a large fraction with another expression above and below the bar, complex fractions marks which bar is the main one. Powers have their own fraction power calculator, roots are in fraction roots, and an unknown x calls for algebraic fractions or fraction equations.
To practice with answers, the order of operations worksheets get harder step by step, from problems with no parentheses to ones that mix powers and mixed numbers. If your mistakes are of another kind, the guide to fraction mistakes sorts them.
As an English-language source, OpenStax’s Prealgebra 2e, Use the Language of Algebra presents the order of operations and the grouping symbols (parentheses, brackets and braces), and says to simplify the innermost grouping first (accessed October 17, 2026).
Frequently asked questions
What does 6/2(1+2) equal?
The calculator works × and ÷ from left to right and treats a product written right next to a parenthesis as one more multiplication, so 6 ÷ 2 × 3 = 9. Other texts read it as 6 ÷ (2 × 3) = 1. Because the notation allows both readings, type the × sign or the parentheses that match what you want to calculate.
How do I type a power of a fraction?
Put the base in parentheses and the exponent after ^, so (3/2)^3 = 27/8. Without parentheses, 3/2^3 raises only the 2 and equals 3/8. Exponents must be integers, positive or negative; a negative one flips the base, as in (4/5)^-1 = 5/4.
How many parentheses can I nest?
The maximum depth is 20, and each parenthesis and each operator to its right counts. In practice you can nest 9 parentheses with one operation at each level, and up to 19 in a row with no operations. Brackets work like parentheses and make groups easier to tell apart, as in ((2/7+3/7)×7)^2 = 5^2 = 25. Braces are not accepted; replace them with parentheses or brackets.
Why do I get an error when I never typed a division by zero?
Because the divisor can turn out to be zero once it is calculated. In 1/(2/5−4/10) the denominator is 2/5 − 4/10 = 0, so the expression is rejected. Check the group under the bar, or the one right after a ÷.