Rollino?
[tex]$b^{\text {th }}$[/tex]
CLASSEVSHEST
Greert suitable Parentheses to make lach statement true
(a) [tex]$16 \times 3-2 \div 4=4$[/tex]
(56) Evaluatu:
Answer (2)
Evaluate the expression without parentheses: 16 × 3 − 2 \tdiv 4 = 47.5 .
Try different placements of parentheses.
Evaluate 16 × ( 3 − 2 ) \tdiv 4 = 4 .
The correct placement of parentheses is 16 × ( 3 − 2 ) \tdiv 4 = 4 .
Explanation
Understanding the Problem We are given the equation 16 × 3 − 2 \tdiv 4 = 4 and we need to insert parentheses to make the equation true. We need to find the correct placement of parentheses to achieve this.
Evaluating without Parentheses Let's evaluate the expression without any parentheses first: 16 × 3 − 2 \tdiv 4 = 48 − 0.5 = 47.5 , which is not equal to 4.
Trying Different Parentheses Placements Now, let's try different placements of parentheses:
( 16 × 3 − 2 ) \tdiv 4 = ( 48 − 2 ) \tdiv 4 = 46 \tdiv 4 = 11.5 , which is not equal to 4.
16 × ( 3 − 2 ) \tdiv 4 = 16 × 1 \tdiv 4 = 16 \tdiv 4 = 4 , which is equal to 4.
16 × 3 − ( 2 \tdiv 4 ) = 48 − 0.5 = 47.5 , which is not equal to 4.
( 16 × 3 ) − 2 \tdiv 4 = 48 − 0.5 = 47.5 , which is not equal to 4.
16 × ( 3 − 2 \tdiv 4 ) = 16 × ( 3 − 0.5 ) = 16 × 2.5 = 40 , which is not equal to 4.
Finding the Correct Placement From the above calculations, we see that the placement of parentheses in the expression 16 × ( 3 − 2 ) \tdiv 4 results in the equation being true, since 16 × ( 3 − 2 ) \tdiv 4 = 16 × 1 \tdiv 4 = 16 \tdiv 4 = 4 .
Conclusion Therefore, the correct placement of parentheses is 16 × ( 3 − 2 ) \tdiv 4 = 4 .
Examples
Parentheses are essential in mathematical expressions to dictate the order of operations. In programming, understanding operator precedence and using parentheses correctly is crucial for writing bug-free code. For example, in calculating the final grade of a student, you might need to ensure that the average of homework scores is calculated before adding it to the exam score, which can be achieved by using parentheses to group the homework scores.
To make the equation 16 × 3 − 2 ÷ 4 = 4 true, we can correctly insert parentheses as 16 × ( 3 − 2 ) ÷ 4 = 4 . This arrangement successfully modifies the order of operations to achieve the desired result. The other placements of parentheses do not yield the same outcome.
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