How would you add parentheses and brackets to make this sentence true:
\[ 45/2 \cdot 4.7 - 4.4 \cdot 6 = 54 \]
Answer (3)
[45/(2 * 4.7) - (4.4)] * 6 = 54
Step 1: PEMDAS (Parenthesis first) 2 × 4.7 = 9.4
Step 2: Still within the parenthesis: 9.4 - 4.4 = 5
Step 3: Finish within the parenthesis: 45 ÷ 5 = 9
Step 4: Last part of the equation: 9 × 6 = 54
Correct placement of brackets and parenthesis to make the statement true is:
[45/(2x4.7)-(4.4)]x6 = 54
The expression 45/2 * 4.7 - 4.4* 6 modified with parentheses and brackets cannot equal 54 under the standard order of operations known as PEMDAS. After evaluating possible rearrangements, none result in the desired outcome of 54, suggesting an error in the original problem or the need for further clarification.
The question you've presented requires us to insert parentheses and possibly brackets into the expression 45/2 * 4.7 - 4.4 * 6 to make it equal to 54. To solve this, we need to apply the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), to structure the expression correctly.
First, let's break down the operations in the given expression without any additional parentheses:
45 divided by 2 equals 22.5.
22.5 times 4.7 equals 105.75.
4.4 times 6 equals 26.4.
105.75 minus 26.4 equals 79.35, which is not equal to 54.
Clearly, we need to add parentheses to change the order of operations. Here's one way to rearrange the expression using parentheses:
((45/2) * 4.7) - (4.4 * 6) = 54
Unfortunately, this does not lead to the correct result as demonstrated above. To make the sentence true, we would need to find the correct placement of parentheses that results in 54 when evaluated.
However, no combination of parentheses will lead us to 54; therefore, there might be a mistake in the original expression or perhaps further clarification of the problem's constraints is required.
To make the equation 2 45 ⋅ 4.7 − 4.4 ⋅ 6 = 54 true, we can rearrange it as [ ( 2 ⋅ 4.7 − 4.4 ) 45 ] ⋅ 6 = 54 . This involves calculating the denominator first and then multiplying by 6 to achieve the desired result. Therefore, the correct brackets and parentheses effectively change the order of operations to yield 54.
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