Asked by Hexx
multiply fractions & decimals quick check answers
Answers
Answered by
Hexx
Use properties of operations and rules for multiplying signed numbers to multiply −25 by 310 . Write the answer in simplest form.(1 point) Responses −650 negative Start Fraction 6 over 50 End Fraction 35 Start Fraction 3 over 5 End Fraction −65 negative Start Fraction 6 over 5 End Fraction −325
Answered by
GPT-4o mini
Sure! Here’s a quick guide to multiply fractions and decimals, along with example problems and their answers.
### Multiplying Fractions
1. **Multiply the Numerators**: Multiply the top numbers (numerators) together.
2. **Multiply the Denominators**: Multiply the bottom numbers (denominators) together.
3. **Simplify the Fraction**: If possible, simplify the resulting fraction.
#### Example Problem:
Multiply \( \frac{2}{3} \times \frac{4}{5} \).
**Solution**:
- Numerators: \( 2 \times 4 = 8 \)
- Denominators: \( 3 \times 5 = 15 \)
- Result: \( \frac{8}{15} \)
### Multiplying Decimals
1. **Ignore the Decimal Points**: Multiply the numbers as if they were whole numbers.
2. **Count Decimal Places**: Count the total number of decimal places in the numbers you multiplied.
3. **Place the Decimal Point**: In your answer, place the decimal point so that it has the same number of decimal places as the total you counted.
#### Example Problem:
Multiply \( 0.6 \times 0.4 \).
**Solution**:
- Ignore the decimal: \( 6 \times 4 = 24 \)
- Count decimal places: \( 0.6 \) has 1 decimal place, \( 0.4 \) has 1 decimal place, for a total of 2 decimal places.
- Place the decimal: \( 0.24 \)
### Quick Check Answers
- **Fraction Example**:
- \( \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \)
- **Decimal Example**:
- \( 0.2 \times 0.5 = 0.1 \)
If you have specific problems you want to check, feel free to share them!
### Multiplying Fractions
1. **Multiply the Numerators**: Multiply the top numbers (numerators) together.
2. **Multiply the Denominators**: Multiply the bottom numbers (denominators) together.
3. **Simplify the Fraction**: If possible, simplify the resulting fraction.
#### Example Problem:
Multiply \( \frac{2}{3} \times \frac{4}{5} \).
**Solution**:
- Numerators: \( 2 \times 4 = 8 \)
- Denominators: \( 3 \times 5 = 15 \)
- Result: \( \frac{8}{15} \)
### Multiplying Decimals
1. **Ignore the Decimal Points**: Multiply the numbers as if they were whole numbers.
2. **Count Decimal Places**: Count the total number of decimal places in the numbers you multiplied.
3. **Place the Decimal Point**: In your answer, place the decimal point so that it has the same number of decimal places as the total you counted.
#### Example Problem:
Multiply \( 0.6 \times 0.4 \).
**Solution**:
- Ignore the decimal: \( 6 \times 4 = 24 \)
- Count decimal places: \( 0.6 \) has 1 decimal place, \( 0.4 \) has 1 decimal place, for a total of 2 decimal places.
- Place the decimal: \( 0.24 \)
### Quick Check Answers
- **Fraction Example**:
- \( \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \)
- **Decimal Example**:
- \( 0.2 \times 0.5 = 0.1 \)
If you have specific problems you want to check, feel free to share them!
Answered by
GPT-4o mini
To multiply \(-25\) by \(310\), we can use the properties of operations and the rules for multiplying signed numbers:
1. **Identify the signs**:
- \(-25\) is negative
- \(310\) is positive
2. **Multiply the absolute values**:
- Multiply \(25\) and \(310\):
\[
25 \times 310 = 7750
\]
3. **Determine the sign of the answer**:
- When multiplying a negative number by a positive number, the result is negative.
4. **Put it all together**:
\[
-25 \times 310 = -7750
\]
Now, let's look at the possible answer choices you've provided:
- **−650**
- **negative Start Fraction 6 over 50 End Fraction**
- **35 Start Fraction 3 over 5 End Fraction**
- **−65**
- **negative Start Fraction 6 over 5 End Fraction**
- **−325**
None of these options correctly represent \(-7750\). If this is in a multiple-choice format, it looks like there might be a mistake in the answer options or the question itself. The correct answer is \(-7750\).
1. **Identify the signs**:
- \(-25\) is negative
- \(310\) is positive
2. **Multiply the absolute values**:
- Multiply \(25\) and \(310\):
\[
25 \times 310 = 7750
\]
3. **Determine the sign of the answer**:
- When multiplying a negative number by a positive number, the result is negative.
4. **Put it all together**:
\[
-25 \times 310 = -7750
\]
Now, let's look at the possible answer choices you've provided:
- **−650**
- **negative Start Fraction 6 over 50 End Fraction**
- **35 Start Fraction 3 over 5 End Fraction**
- **−65**
- **negative Start Fraction 6 over 5 End Fraction**
- **−325**
None of these options correctly represent \(-7750\). If this is in a multiple-choice format, it looks like there might be a mistake in the answer options or the question itself. The correct answer is \(-7750\).