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order of operations arithmetic

Check the final answer first, then review the worked steps.

Problem

order of operations arithmetic

Answer

1

Step-by-step solution

To solve the expression $9 - 3 \div \frac{1}{3} + 1$, we must follow the order of operations, commonly known as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right).

  1. Perform the division: According to the order of operations, division must be performed before addition and subtraction. We need to calculate $3 \div \frac{1}{3}$. Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of $\frac{1}{3}$ is $3$. Therefore, $3 \div \frac{1}{3} = 3 \times 3 = 9$.
  1. Substitute the result back into the expression: Now replace $3 \div \frac{1}{3}$ with $9$ in the original expression: $9 - 9 + 1$.
  1. Perform addition and subtraction from left to right: Now we evaluate the remaining operations in order from left to right. First, $9 - 9 = 0$. Then, $0 + 1 = 1$.