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Worked Examples

Place Grouping Symbols

Practice changing the value of an expression.

Where can parentheses be placed in the expression so that it has a value of [tex]$26$[/tex]?

[tex]\[ 4 + 2 \cdot 14 - 3 \][/tex]

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Sagot :

GinnyAnsweridn
To achieve the value of 26 from the expression [tex]\( 4 + 2 \cdot 14 - 3 \)[/tex], we need to carefully place parentheses to control the order of operations. Here is a step-by-step explanation:

1. Identify the operations and their default order: The given expression is [tex]\( 4 + 2 \cdot 14 - 3 \)[/tex]. According to the order of operations (PEMDAS/BODMAS), multiplication and division are performed before addition and subtraction.

2. Reevaluate to influence the result: We want the final result to be 26. Consider where you could place parentheses to change the order of operations:

[tex]\[ 4 + 2 \cdot (14 - 3) \][/tex]

3. Evaluate the expression within the parentheses:
[tex]\[ 14 - 3 = 11 \][/tex]

4. Continue with multiplication:
[tex]\[ 2 \cdot 11 = 22 \][/tex]

5. Finish with addition:
[tex]\[ 4 + 22 = 26 \][/tex]

By placing the parentheses around [tex]\( 14 - 3 \)[/tex], the expression changes to [tex]\( 4 + 2 \cdot (14 - 3) \)[/tex]. This ensures the subtraction is done first, followed by multiplication, and finally addition, resulting in the desired value of 26.

So, the expression with parentheses placed to achieve a value of 26 is:
[tex]\[ 4 + 2 \cdot (14 - 3) \][/tex]
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