9 - 3 ÷ (1/3) + 1 = ?
Understand the Problem
The question involves performing arithmetic operations according to the order of operations (PEMDAS/BODMAS) to find the value of the expression given.
Answer
The answer is $1$.
Answer for screen readers
The final answer is $1$.
Steps to Solve
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Identify the operations needed We need to calculate the expression step by step, following the order of operations (PEMDAS/BODMAS). This means we will handle division before subtraction and addition.
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Calculate the division The expression includes a division: $$ 3 \div \frac{1}{3} $$
Dividing by a fraction is the same as multiplying by its reciprocal: $$ \frac{3}{1} \times \frac{3}{1} = 9 $$
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Rewrite the expression Now substitute this result back into the expression: $$ 9 - 9 + 1 $$
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Perform the subtraction Next, calculate: $$ 9 - 9 = 0 $$
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Perform the final addition Now add 1 to the result: $$ 0 + 1 = 1 $$
The final answer is $1$.
More Information
This problem illustrates the importance of following the order of operations in arithmetic. When dividing by a fraction, it can sometimes be overlooked, but it can change the result significantly. The expression simplifies nicely when each step is calculated carefully.
Tips
- Ignoring order of operations: Always perform division before subtraction and addition.
- Miscalculating the division with fractions: Remember that dividing by a fraction means multiplying by its reciprocal.
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