$30 \div \frac{1}{3} \times \frac{1}{3}$
Answer (2)
The expression 30 ÷ 3 1 × 3 1 simplifies to 30 . First, we rewrite the division as multiplication, yielding 30 × 3 × 3 1 . Upon performing the multiplications, we find the final answer is 30 .
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Rewrite the division as multiplication: 30 × 3 × 3 1 .
Multiply 30 by 3 : 90 × 3 1 .
Multiply 90 by 3 1 : 3 90 = 30 .
The final result is 30 .
Explanation
Understanding the Expression We are asked to evaluate the expression 30 ÷ 3 1 × 3 1 . Remember the order of operations (PEMDAS/BODMAS), which tells us to perform division and multiplication from left to right.
Rewriting Division First, we rewrite the division as multiplication by the reciprocal: 30 ÷ 3 1 = 30 × 3 . So the expression becomes 30 × 3 × 3 1 .
First Multiplication Next, we perform the first multiplication: 30 × 3 = 90 . The expression is now 90 × 3 1 .
Second Multiplication Finally, we perform the last multiplication: 90 × 3 1 = 3 90 = 30 .
Final Answer Therefore, the value of the expression 30 ÷ 3 1 × 3 1 is 30.
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating discounts or figuring out ingredient ratios in a recipe. For instance, if you have a coupon for 1/3 off an item and then another 1/3 off the discounted price, you need to calculate it correctly to know the final price. The expression 30 ÷ 3 1 × 3 1 is similar to calculating a price after successive discounts or increases, where the order of operations matters significantly to get the correct result. Correctly applying the order of operations ensures accurate financial calculations and helps avoid misunderstandings in everyday transactions.
