Final answer:
The expression ⅓[4÷(7-4)] simplifies to 1 using the order of operations: calculate the difference in parentheses, divide, and then multiply by ⅓.
Step-by-step explanation:
To solve the expression ⅓[4÷(7-4)], we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition, and Subtraction from left to right).
- First, solve the expression inside the parentheses (7-4), which equals 3.
- Next, divide 4 by the result in step 1, which is 4 ÷ 3, resulting in ⅔ or 1.3333 if written as a decimal.
- Finally, multiply ¾ by the result from step 2, so ¾ × ⅔ equals 1. To understand why, think of ¾ as 3 quarters of something and ⅔ as the whole of that same 'something'. Hence, 3 quarters of 1 whole is indeed 1.
To solve the expression 3/4[4÷(7-4)], we need to follow the order of operations, which is parentheses, multiplication/division from left to right, and finally addition/subtraction from left to right. Here's the step-by-step solution:
Start by evaluating the expression inside the parentheses. 7 - 4 = 3.
Next, divide 4 by 3: 4 ÷ 3 = 1.33 (rounded to two decimal places).
Multiply 3/4 by 1.33: 3/4 * 1.33 = 0.99 (rounded to two decimal places).
Therefore, the simplified value of the expression 3/4[4÷(7-4)] is approximately 0.99.