Arithmetic

2x3+902/78-(8932x8394)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

Identify the order of operations

We follow PEMDAS: Parentheses first, then Multiplication and Division left to right, then Addition and Subtraction left to right. This is an arithmetic expression, not an equation, so we simplify it to one number.

Solve the parentheses: multiply 8932 × 8394

We handle the parentheses first. Multiplying 8932 by 8394 gives 74,955,208.

Multiply 2 × 3 (left side)

Next we handle the multiplication outside the parentheses. 2 times 3 equals 6.

Divide 902 ÷ 78

We simplify the division. 902 divided by 78 simplifies to 451/39, which is approximately 11.5641. We'll keep the fraction for exactness.

Combine all terms left to right

Now we add and subtract the results from left to right. We have 6 plus 451/39 minus 74,955,208.

Convert 6 to a fraction and add

To add 6 and 451/39, convert 6 to 234/39. Then 234 + 451 = 685, giving us 685/39.

Subtract 74,955,208 and simplify

Convert 74,955,208 to a fraction over 39: 74,955,208 × 39 = 2,923,253,112. Subtract: 685 − 2,923,253,112 = −2,923,252,427. Dividing gives approximately −74,955,190.436.

Understanding this problem

Learning Insight

PEMDAS (order of operations) exists so every person gets the same answer from the same expression. Without a shared set of rules, the same string of numbers and symbols could mean different things to different people. The parentheses here force the big multiplication to happen before the subtraction.

Quick Tip

When you see a huge multiplication inside parentheses being subtracted, do that big multiplication first — it will almost always dominate the final answer and make it very negative or very large.

Common Mistake

Students often do the operations strictly left to right and compute 2×3+902 first before dividing by 78, ignoring that division must be handled before addition according to PEMDAS.