Which expression has the same value as the one below?
[tex]$8+[4+(-9)][/tex]
[tex]$12+(-9)$[/tex]
[tex]$-12+9$[/tex]
[tex]$-4+(-9)$[/tex]
[tex]$4+(-9)$[/tex]
Answer (2)
First, simplify the original expression: 8 + [ 4 + ( − 9 )] = 8 + [ 4 − 9 ] = 8 + ( − 5 ) = 3 .
Then, simplify each of the options.
12 + ( − 9 ) = 12 − 9 = 3 .
The expression with the same value is 12 + ( − 9 ) .
Explanation
Simplify the given expression We are asked to find the expression that has the same value as 8 + [ 4 + ( − 9 )] . Let's first simplify the given expression.
Simplify inside the brackets First, we simplify the expression inside the brackets: 4 + ( − 9 ) . Since we are adding a negative number, it's the same as subtracting: 4 − 9 = − 5 .
Calculate the value of the expression Now we substitute this back into the original expression: 8 + ( − 5 ) . Again, adding a negative number is the same as subtracting: 8 − 5 = 3 . So, the value of the given expression is 3.
Check each option Now we need to check each of the given options to see which one also equals 3.
Option 1: 12 + ( − 9 ) = 12 − 9 = 3 . This is equal to 3. Option 2: − 12 + 9 = − 3 . This is not equal to 3. Option 3: − 4 + ( − 9 ) = − 4 − 9 = − 13 . This is not equal to 3. Option 4: 4 + ( − 9 ) = 4 − 9 = − 5 . This is not equal to 3.
Final Answer Therefore, the expression that has the same value as 8 + [ 4 + ( − 9 )] is 12 + ( − 9 ) .
Examples
Understanding how to simplify expressions with positive and negative numbers is useful in many real-life situations. For example, if you are managing a budget, you might have income (positive numbers) and expenses (negative numbers). Simplifying expressions helps you calculate your net balance. Another example is when calculating temperature changes. If the temperature drops, it's represented by a negative number, and simplifying expressions helps you find the final temperature.
The expression 8 + [ 4 + ( − 9 )] simplifies to 3. The only option that also equals 3 is 12 + ( − 9 ) . Therefore, the answer is 12 + ( − 9 ) .
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