Calculate the value of the expression:
16 ÷ 4 of 4 × [3 ÷ 4 of {4 × 3 ÷ (3 + 3)}] ÷ (2 ÷ 4 of 8)
Answer (2)
By following the order of operations (PEMDAS), we break down the expression step by step and calculate each part systematically. After resolving all operations, the final value of the expression is 1.5. This process involves evaluating parentheses first, followed by division and multiplication in the correct order.
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To solve the expression 16 ÷ 4 of 4 × [ 3 ÷ 4 of { 4 × 3 ÷ ( 3 + 3 )}] ÷ ( 2 ÷ 4 of 8 ) , we'll need to follow the order of operations, often remembered as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).
Let's proceed step-by-step:
Simplify inside the smallest brackets (parentheses) :
( 3 + 3 ) = 6 .
Move on to the curly braces :
Substitute 6 back into the expression: 4 × 3 ÷ 6 .
Calculate inside the curly braces: 4 × 3 = 12 and 12 ÷ 6 = 2 .
Thus, {4 \times 3 \div (3 + 3)} evaluates to 2 .
Solve inside the square brackets :
Substitute 2 back into: 3 ÷ 4 of 2 .
Calculate the 'of' operation (which indicates multiplication): 4 of 2 = 8 .
Calculate: 3 ÷ 8 = 0.375 .
So the term [ 3 ÷ 4 of { 4 × 3 ÷ ( 3 + 3 )}] evaluates to 0.375 .
Calculate the division and multiplication for the main expression :
The expression simplifies to: 16 ÷ 4 of 4 × 0.375 ÷ ( 2 ÷ 4 of 8 ) .
Calculate the denominator :
4 of 8 = 32 (since 'of' implies multiplication).
2 ÷ 32 = 0.0625 .
Complete the remaining calculations :
First perform 4 of 4 = 16 .
Then 16 ÷ 16 = 1 .
And 1 × 0.375 = 0.375 .
Finally, 0.375 ÷ 0.0625 = 6 .
So the value of the expression is 6 .
