Question
Use the additive inverse to find −123.45−(−234.76).(1 point)
111.31
111.31
−358.21
negative 358.21
121.31
121.31
−111.31
negative 111.31
111.31
111.31
−358.21
negative 358.21
121.31
121.31
−111.31
negative 111.31
Answers
GPT-4o mini
To solve the expression \(-123.45 - (-234.76)\), we can use the property of the additive inverse.
The additive inverse of a number \(x\) is \(-x\). Therefore, subtracting a negative number is the same as adding its positive counterpart:
\[
-123.45 - (-234.76) = -123.45 + 234.76
\]
Now, let's calculate it:
\[
-123.45 + 234.76 = 234.76 - 123.45
\]
Performing the subtraction:
\[
234.76 - 123.45 = 111.31
\]
Thus, the result of the expression \(-123.45 - (-234.76)\) is:
\[
111.31
\]
So, the answer is **111.31**.
The additive inverse of a number \(x\) is \(-x\). Therefore, subtracting a negative number is the same as adding its positive counterpart:
\[
-123.45 - (-234.76) = -123.45 + 234.76
\]
Now, let's calculate it:
\[
-123.45 + 234.76 = 234.76 - 123.45
\]
Performing the subtraction:
\[
234.76 - 123.45 = 111.31
\]
Thus, the result of the expression \(-123.45 - (-234.76)\) is:
\[
111.31
\]
So, the answer is **111.31**.
Use the additive inverse to find −2445−6710.(1 point)
Responses
31 1/2
31 Start Fraction 1 over 2 End Fraction
−18 1 10
negative 18 Start Fraction 1 over 10 End Fraction
−31 1/2
negative 31 Start Fraction 1 over 2 End Fraction
−31 1/10
Responses
31 1/2
31 Start Fraction 1 over 2 End Fraction
−18 1 10
negative 18 Start Fraction 1 over 10 End Fraction
−31 1/2
negative 31 Start Fraction 1 over 2 End Fraction
−31 1/10
GPT-4o mini
To solve the expression \(-2445 - 6710\) using the additive inverse, we rewrite it as:
\[
-2445 - 6710 = -2445 + (-6710)
\]
Now, we'll find the sum of these two negative numbers:
\[
-2445 + (-6710) = -(2445 + 6710)
\]
Next, let's add \(2445\) and \(6710\):
\[
2445 + 6710 = 9155
\]
Thus, we have:
\[
-2445 - 6710 = -9155
\]
Now let's check the provided options:
- **31 1/2**
- **−18 1 10**
- **−31 1/2**
- **−31 1/10**
None of these options match \(-9155\), indicating there might be a misunderstanding or error in the provided choices. If there was a typo or another operator accidentally included in the question, do let me know!
However, based on the calculations, the answer is:
\(-9155\).
\[
-2445 - 6710 = -2445 + (-6710)
\]
Now, we'll find the sum of these two negative numbers:
\[
-2445 + (-6710) = -(2445 + 6710)
\]
Next, let's add \(2445\) and \(6710\):
\[
2445 + 6710 = 9155
\]
Thus, we have:
\[
-2445 - 6710 = -9155
\]
Now let's check the provided options:
- **31 1/2**
- **−18 1 10**
- **−31 1/2**
- **−31 1/10**
None of these options match \(-9155\), indicating there might be a misunderstanding or error in the provided choices. If there was a typo or another operator accidentally included in the question, do let me know!
However, based on the calculations, the answer is:
\(-9155\).
Use the additive inverse to find −24 4/5−6 7/10.(1 point)
Responses
31 1/2
31 Start Fraction 1 over 2 End Fraction
−18 1 10
negative 18 Start Fraction 1 over 10 End Fraction
−31 1/2
negative 31 Start Fraction 1 over 2 End Fraction
−31 1/10
Responses
31 1/2
31 Start Fraction 1 over 2 End Fraction
−18 1 10
negative 18 Start Fraction 1 over 10 End Fraction
−31 1/2
negative 31 Start Fraction 1 over 2 End Fraction
−31 1/10
GPT-4o mini
To solve the expression \(-24 \frac{4}{5} - 6 \frac{7}{10}\) using the additive inverse, we first convert the mixed numbers into improper fractions.
1. **Convert \(-24 \frac{4}{5}\) to an improper fraction**:
\[
-24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\left(120 + 4\right)/5 = -\frac{124}{5}
\]
2. **Convert \(-6 \frac{7}{10}\) to an improper fraction**:
\[
-6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\left(60 + 7\right)/10 = -\frac{67}{10}
\]
Next, we need a common denominator to add these fractions. The least common multiple (LCM) of 5 and 10 is 10.
3. **Convert \(-\frac{124}{5}\) to a fraction with a denominator of 10**:
\[
-\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10}
\]
4. **Now perform the addition**:
\[
-\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}
\]
Now, let's simplify \(-\frac{315}{10}\):
\[
-\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2}
\]
Now we look at the answer choices:
- **31 1/2**
- **−18 1 10**
- **−31 1/2**
- **−31 1/10**
The correct choice is **−31 1/2**.
1. **Convert \(-24 \frac{4}{5}\) to an improper fraction**:
\[
-24 \frac{4}{5} = -\left(24 \times 5 + 4\right)/5 = -\left(120 + 4\right)/5 = -\frac{124}{5}
\]
2. **Convert \(-6 \frac{7}{10}\) to an improper fraction**:
\[
-6 \frac{7}{10} = -\left(6 \times 10 + 7\right)/10 = -\left(60 + 7\right)/10 = -\frac{67}{10}
\]
Next, we need a common denominator to add these fractions. The least common multiple (LCM) of 5 and 10 is 10.
3. **Convert \(-\frac{124}{5}\) to a fraction with a denominator of 10**:
\[
-\frac{124}{5} = -\frac{124 \times 2}{5 \times 2} = -\frac{248}{10}
\]
4. **Now perform the addition**:
\[
-\frac{248}{10} - \frac{67}{10} = -\frac{248 + 67}{10} = -\frac{315}{10}
\]
Now, let's simplify \(-\frac{315}{10}\):
\[
-\frac{315}{10} = -31 \frac{5}{10} = -31 \frac{1}{2}
\]
Now we look at the answer choices:
- **31 1/2**
- **−18 1 10**
- **−31 1/2**
- **−31 1/10**
The correct choice is **−31 1/2**.