Answer :
Let's evaluate each expression step-by-step and determine which expressions are equivalent.
1. First row expressions:
- Expression: [tex]\(-21 + 94\)[/tex]
- Calculate: [tex]\(-21 + 94 = 73\)[/tex]
- Compare with: [tex]\(94 - 21\)[/tex]
- Calculate: [tex]\(94 - 21 = 73\)[/tex]
Both expressions in the first row evaluate to 73. So, they are equivalent.
2. Second row expression:
- Expression: [tex]\(21 - (-94)\)[/tex]
- When you subtract a negative number, it's the same as adding the positive version of that number.
- So, [tex]\(21 - (-94) = 21 + 94 = 115\)[/tex]
This does not match the value from the first row (73). Therefore, it's not equivalent to either expression in the first row.
3. Third row expression:
- Expression: [tex]\(94 + (-21)\)[/tex]
- Adding a negative number is the same as subtracting the positive number.
- So, [tex]\(94 + (-21) = 94 - 21 = 73\)[/tex]
This matches the value from the first row (73). Therefore, it's equivalent to both expressions in the first row.
In summary:
- The first and third expressions evaluate to 73 and are equivalent to each other.
- The second expression evaluates to 115 and is not equivalent to the others.
1. First row expressions:
- Expression: [tex]\(-21 + 94\)[/tex]
- Calculate: [tex]\(-21 + 94 = 73\)[/tex]
- Compare with: [tex]\(94 - 21\)[/tex]
- Calculate: [tex]\(94 - 21 = 73\)[/tex]
Both expressions in the first row evaluate to 73. So, they are equivalent.
2. Second row expression:
- Expression: [tex]\(21 - (-94)\)[/tex]
- When you subtract a negative number, it's the same as adding the positive version of that number.
- So, [tex]\(21 - (-94) = 21 + 94 = 115\)[/tex]
This does not match the value from the first row (73). Therefore, it's not equivalent to either expression in the first row.
3. Third row expression:
- Expression: [tex]\(94 + (-21)\)[/tex]
- Adding a negative number is the same as subtracting the positive number.
- So, [tex]\(94 + (-21) = 94 - 21 = 73\)[/tex]
This matches the value from the first row (73). Therefore, it's equivalent to both expressions in the first row.
In summary:
- The first and third expressions evaluate to 73 and are equivalent to each other.
- The second expression evaluates to 115 and is not equivalent to the others.
