What is the answer with PEMDAS?

How it works

Reading the expression. You can type numbers (digits with an optional decimal point, such as 12, 0.25 or .5, read exactly), the operations +, - (or −), * (or ×, ·, x), / (or ÷), ^ (or **), and brackets ( ), [ ] or { } (each must be closed by the same kind). A minus sign in front of something makes it negative, and a plus sign in front of something is ignored (+3, 2 ++ 3). A bracket right after a number or a closing bracket means multiply: 2(3 + 4) is 2 × (3 + 4). A number right after a closing bracket needs a sign: (2 + 3)4 gives a message, (2 + 3) × 4 works. Two numbers side by side, commas, and other characters are not allowed.

Rank of the operations. From highest to lowest:

1. Parentheses (brackets): what is inside is worked out first.
2. Exponents. They group from the right: 2^3^2 is 2^(3^2). An exponent binds tighter than a minus sign in front: -3^2 is -(3^2) = −9, while 2^-2 is 2^(-2).
3. Multiplication and division, equal rank, from left to right. A multiplication written without a sign has the same rank as ×, so 8 ÷ 2(2 + 2) is 8 ÷ 2 × (2 + 2) = 16.
4. Addition and subtraction, equal rank, from left to right.

One operation per step. An operation is ready when both of its sides are single numbers. At each step the calculator picks one ready operation:

1. the one inside the most parentheses (the deepest);
2. among those, the one in the leftmost pair of parentheses (or outside all parentheses, if none);
3. among those, the highest rank: exponent, then × and ÷, then + and −;
4. among those, the leftmost.

It replaces that operation with its exact value. Parentheses around a single number are then dropped, and a minus sign in front of a number joins the number (−(−3) is 3).

Exact values. All values are exact fractions. Exponents must be whole numbers; a negative exponent gives the reciprocal (2^(-2) = 0.25). 0^0, division by 0, and 0 to a negative power have no answer, and two size rules keep answers exact and quick. Let the size of a fraction p/q be the number of binary digits of |p| plus that of q (a whole number n is n/1, and 1 has 1 binary digit). A power a^e, other than 0, 1 or −1 to any power, gives no answer ("too large to show exactly") when |e| × the size of a is more than 100,000: 2^33333 (3 × 33,333 = 99,999) works and 2^33334 does not. Any step whose result has a size over 100,000 gives no answer too.

The calculator shows:

• Answer: a whole number (14), a decimal that ends, written in full (0.7, -2.75), or else a fraction in lowest terms (7/12, -1/3). A minus sign is a plain hyphen, with no thousands separators.
• As a decimal: only when the answer is a fraction: its decimal value (the nearest 64-bit float), shown to at most 6 decimal places. It is left out when that value is beyond the largest 64-bit float (about 1.8 × 10^308, as for 2^1100 ÷ 3); the exact fraction is still the answer.
• Read as: the expression as the calculator reads it, before the first step: parentheses around a single number are dropped and a minus sign in front of a number joins it (2(3)(-4) is read as 2 × 3 × (-4)), and it is written the same way as the steps.
• Steps, joined by a semicolon and a space. Each step is <Operation>: <left> <sign> <right> = <value>, followed by , so <the whole expression now> unless the expression is now a single number. The operation words are Exponent, Multiply, Divide, Add and Subtract, followed by inside the parentheses when the operation is inside at least one pair of parentheses. An expression that is a single number has the one step There is nothing to work out: the expression is a single number.
• Note: shown when a multiplication written without a sign comes after a ÷ in the same run of × and ÷ (as in 8 ÷ 2(2 + 2)). It reads: "A multiplication written without a sign, as in 2(3 + 1), counts as an ordinary × here and is done left to right with ÷. To multiply first, put the product in parentheses."

How expressions are written (in the steps and in "Read as"): the signs are +, − (U+2212), × and ÷ with a space on each side, and ^ with no spaces. All brackets are written as round parentheses. A number is written as in the answer; a fraction is always put in parentheses ((1/3) × 3), and a negative number is put in parentheses unless it is the first thing in the expression or in a pair of parentheses (2 − (-2), -9 + 1). The base of an exponent is put in parentheses when it is negative or a fraction ((-3)^2). A minus sign in front of a group or an exponent is written - right before it (-(2 + 3), -3^2).

Worked examples by hand

3 + 6 × (5 + 4) ÷ 3 − 7. Parentheses: 5 + 4 = 9, giving 3 + 6 × 9 ÷ 3 − 7. Multiply and divide from the left: 6 × 9 = 54, then 54 ÷ 3 = 18, giving 3 + 18 − 7. Add and subtract from the left: 3 + 18 = 21, then 21 − 7 = 14.

3 + 4 × 2 − 6 ÷ 3. 4 × 2 = 8 and 6 ÷ 3 = 2 come first: 3 + 8 − 2 = 9.

8 ÷ 2(2 + 2). Parentheses: 2 + 2 = 4, giving 8 ÷ 2 × 4. Left to right: 8 ÷ 2 = 4, then 4 × 4 = 16.

−3^2 + (1 − 4)^2. Parentheses: 1 − 4 = −3, giving −3^2 + (−3)^2. Exponents, left first: 3^2 = 9, so −9 + (−3)^2; then (−3)^2 = 9, so −9 + 9 = 0.

2^3^2. Exponents group from the right: 3^2 = 9, then 2^9 = 512.

1 ÷ 3 + 1 ÷ 4. 1 ÷ 3 = 1/3 (kept as a fraction), 1 ÷ 4 = 0.25, and 1/3 + 1/4 = 4/12 + 3/12 = 7/12, about 0.583333.

(2 + 1) ÷ 9. 2 + 1 = 3, and 3 ÷ 9 = 1/3, about 0.333333.

0.1 + 0.2 × 3. 0.2 × 3 = 0.6, then 0.1 + 0.6 = 0.7, exactly.