Question

Which expression is equivalent to

A
2.2−(−2.5)2.2-\left(-2.5\right)2.2−(−2.5)
B
2.2+(−2.5)2.2+\left(-2.5\right)2.2+(−2.5)
C
2.5−2.22.5-2.22.5−2.2
D
2.2+2.52.2+2.52.2+2.5

Answer 1

−10 − (−21)

Answer 2

−10 − (−21) additive inverse

Answer 3

-3/12-2/5

Answer 4

-3/15-2/5

Answer 5

pls do it again but turn the denominators to common denominators

Answer 6

To determine which expression is equivalent to \( 2.2 - (-2.5) \), we can simplify it:

1. **Evaluate \( 2.2 - (-2.5) \)**:
\[
2.2 - (-2.5) = 2.2 + 2.5
\]
This is because subtracting a negative number is the same as adding its positive counterpart.

Now, let's compare this simplification with the provided options:

- **Option A**: \( 2.2 - (-2.5) \) is actually the original expression, which simplifies to \( 2.2 + 2.5 \).

- **Option B**: \( 2.2 + (-2.5) \) simplifies to \( 2.2 - 2.5 \), which is not equivalent to \( 2.2 + 2.5 \).

- **Option C**: \( 2.5 - 2.2 \) simplifies to \( 0.3 \), which is also not equivalent.

- **Option D**: \( 2.2 + 2.5 \) is exactly what we obtained after simplifying the original expression.

Thus, the correct answer is **D** \( 2.2 + 2.5 \).

Answer 7

To simplify the expression \( -10 - (-21) \), you can follow these steps:

1. **Recognize that subtracting a negative number is the same as adding its positive counterpart**:
\[
-10 - (-21) = -10 + 21
\]

2. **Perform the addition**:
\[
-10 + 21 = 11
\]

Therefore, the result of \( -10 - (-21) \) is \( 11 \).

Answer 8

The additive inverse of a number \(x\) is the number that, when added to \(x\), yields zero.

To find the additive inverse of \( -10 - (-21) \), we first simplify the expression:

1. **Simplify the expression**:
\[
-10 - (-21) = -10 + 21 = 11
\]

2. **Now, find the additive inverse of \( 11 \)**:
The additive inverse of \( 11 \) is \( -11 \), because:
\[
11 + (-11) = 0
\]

So, the additive inverse of \( -10 - (-21) \) (which is \( 11 \)) is \( -11 \).

Answer 9

To simplify the expression \(-\frac{3}{12} - \frac{2}{5}\), we need to follow these steps:

1. **Simplify \(-\frac{3}{12}\)**:
\[
-\frac{3}{12} = -\frac{1}{4}
\]
(This is done by dividing the numerator and the denominator by their greatest common divisor, which is 3.)

2. **Now, rewrite the expression**:
\[
-\frac{1}{4} - \frac{2}{5}
\]

3. **Find a common denominator**:
The least common multiple of 4 and 5 is 20.

4. **Convert each fraction**:
\[
-\frac{1}{4} = -\frac{5}{20} \quad \text{(multiply numerator and denominator by 5)}
\]
\[
-\frac{2}{5} = -\frac{8}{20} \quad \text{(multiply numerator and denominator by 4)}
\]

5. **Now combine the fractions**:
\[
-\frac{5}{20} - \frac{8}{20} = -\frac{5 + 8}{20} = -\frac{13}{20}
\]

Therefore, the final answer is:
\[
-\frac{13}{20}
\]

Answer 10

To simplify the expression \(-\frac{3}{15} - \frac{2}{5}\), follow these steps:

1. **Simplify \(-\frac{3}{15}\)**:
\[
-\frac{3}{15} = -\frac{1}{5}
\]
(This is done by dividing the numerator and the denominator by their greatest common divisor, which is 3.)

2. **Now, rewrite the expression**:
\[
-\frac{1}{5} - \frac{2}{5}
\]

3. **Combine the fractions**:
Since the denominators are the same, you can simply add the numerators:
\[
-\frac{1}{5} - \frac{2}{5} = -\frac{1 + 2}{5} = -\frac{3}{5}
\]

Therefore, the final answer is:
\[
-\frac{3}{5}
\]

Answer 11

Sure! Let's rewrite the expression \(-\frac{3}{15} - \frac{2}{5}\) using a common denominator:

1. **Identify the denominators**: The denominators are 15 and 5.

2. **Find the common denominator**: The least common multiple (LCM) of 15 and 5 is 15.

3. **Convert \(-\frac{2}{5}\) to have a denominator of 15**:
\[
-\frac{2}{5} = -\frac{2 \cdot 3}{5 \cdot 3} = -\frac{6}{15}
\]

4. **Now rewrite the expression**:
\[
-\frac{3}{15} - \frac{6}{15}
\]

5. **Combine the fractions**:
\[
-\frac{3}{15} - \frac{6}{15} = -\frac{3 + 6}{15} = -\frac{9}{15}
\]

6. **Simplify \(-\frac{9}{15}\)**:
The greatest common divisor of 9 and 15 is 3, so we can simplify:
\[
-\frac{9 \div 3}{15 \div 3} = -\frac{3}{5}
\]

Thus, the final answer, using the method with common denominators, is:
\[
-\frac{3}{5}
\]