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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

11 answers

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 \( 2.2 + 2.5 \).

−10 − (−21)

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 \( 11 \).

−10 − (−21) additive inverse

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 \( -11 \).

-3/12-2/5

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: \[ -\frac{13}{20} \]

-3/15-2/5

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: \[ -\frac{3}{5} \]

pls do it again but turn the denominators to common denominators

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: \[ -\frac{3}{5} \]