Question
how to turn 2/3/8 in a improper fraction
Answers
Answer
how to multiply fractions
Answer
3/8 x 2/3/8
Answer
8-6/5/5
Answer
8-6/3/5
Answer
how to find prime fractoration 720
Answered by
GPT-4o mini
To convert the mixed number \(2 \frac{3}{8}\) into an improper fraction, follow these steps:
1. Multiply the whole number (2) by the denominator of the fractional part (8).
\[
2 \times 8 = 16
\]
2. Add the result to the numerator of the fractional part (3).
\[
16 + 3 = 19
\]
3. Place this result over the original denominator (8).
\[
\frac{19}{8}
\]
So, \(2 \frac{3}{8}\) as an improper fraction is \(\frac{19}{8}\).
1. Multiply the whole number (2) by the denominator of the fractional part (8).
\[
2 \times 8 = 16
\]
2. Add the result to the numerator of the fractional part (3).
\[
16 + 3 = 19
\]
3. Place this result over the original denominator (8).
\[
\frac{19}{8}
\]
So, \(2 \frac{3}{8}\) as an improper fraction is \(\frac{19}{8}\).
Answered by
GPT-4o mini
To multiply fractions, follow these simple steps:
1. **Multiply the numerators**: Multiply the top numbers (numerators) of the fractions together to get the new numerator.
2. **Multiply the denominators**: Multiply the bottom numbers (denominators) of the fractions together to get the new denominator.
3. **Simplify the fraction (if necessary)**: If the resulting fraction can be simplified, do so by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number.
### Example:
Multiply the fractions \(\frac{2}{3}\) and \(\frac{4}{5}\):
1. **Multiply the numerators**:
\[
2 \times 4 = 8
\]
2. **Multiply the denominators**:
\[
3 \times 5 = 15
\]
3. **Combine to form the new fraction**:
\[
\frac{8}{15}
\]
4. **Simplifying (if applicable)**: In this case, \(\frac{8}{15}\) is already in its simplest form.
So, \(\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}\).
1. **Multiply the numerators**: Multiply the top numbers (numerators) of the fractions together to get the new numerator.
2. **Multiply the denominators**: Multiply the bottom numbers (denominators) of the fractions together to get the new denominator.
3. **Simplify the fraction (if necessary)**: If the resulting fraction can be simplified, do so by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number.
### Example:
Multiply the fractions \(\frac{2}{3}\) and \(\frac{4}{5}\):
1. **Multiply the numerators**:
\[
2 \times 4 = 8
\]
2. **Multiply the denominators**:
\[
3 \times 5 = 15
\]
3. **Combine to form the new fraction**:
\[
\frac{8}{15}
\]
4. **Simplifying (if applicable)**: In this case, \(\frac{8}{15}\) is already in its simplest form.
So, \(\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}\).
Answered by
GPT-4o mini
It seems like you want to multiply the fraction \(\frac{3}{8}\) by the mixed number \(2\frac{3}{8}\). To do this, we first need to convert the mixed number into an improper fraction.
### Step 1: Convert \(2 \frac{3}{8}\) to an improper fraction.
1. Multiply the whole number by the denominator:
\[
2 \times 8 = 16
\]
2. Add the numerator:
\[
16 + 3 = 19
\]
3. Write it as an improper fraction:
\[
2 \frac{3}{8} = \frac{19}{8}
\]
### Step 2: Multiply \(\frac{3}{8}\) by \(\frac{19}{8}\).
Now, we multiply:
\[
\frac{3}{8} \times \frac{19}{8}
\]
1. **Multiply the numerators**:
\[
3 \times 19 = 57
\]
2. **Multiply the denominators**:
\[
8 \times 8 = 64
\]
3. **Combine to form the new fraction**:
\[
\frac{57}{64}
\]
So, \(\frac{3}{8} \times 2\frac{3}{8} = \frac{57}{64}\). This fraction is already in its simplest form.
### Step 1: Convert \(2 \frac{3}{8}\) to an improper fraction.
1. Multiply the whole number by the denominator:
\[
2 \times 8 = 16
\]
2. Add the numerator:
\[
16 + 3 = 19
\]
3. Write it as an improper fraction:
\[
2 \frac{3}{8} = \frac{19}{8}
\]
### Step 2: Multiply \(\frac{3}{8}\) by \(\frac{19}{8}\).
Now, we multiply:
\[
\frac{3}{8} \times \frac{19}{8}
\]
1. **Multiply the numerators**:
\[
3 \times 19 = 57
\]
2. **Multiply the denominators**:
\[
8 \times 8 = 64
\]
3. **Combine to form the new fraction**:
\[
\frac{57}{64}
\]
So, \(\frac{3}{8} \times 2\frac{3}{8} = \frac{57}{64}\). This fraction is already in its simplest form.
Answered by
GPT-4o mini
To evaluate the expression \(8 - \frac{6}{5} \div 5\), we need to follow the order of operations:
1. **Calculate the division part first**:
\[
\frac{6}{5} \div 5
\]
To divide by a whole number, you can multiply by the reciprocal:
\[
\frac{6}{5} \div 5 = \frac{6}{5} \times \frac{1}{5} = \frac{6 \times 1}{5 \times 5} = \frac{6}{25}
\]
2. **Now substitute this back into the expression**:
\[
8 - \frac{6}{25}
\]
3. **Convert 8 to a fraction with a denominator of 25**:
\[
8 = \frac{8 \times 25}{1 \times 25} = \frac{200}{25}
\]
4. **Now subtract \(\frac{6}{25}\) from \(\frac{200}{25}\)**:
\[
\frac{200}{25} - \frac{6}{25} = \frac{200 - 6}{25} = \frac{194}{25}
\]
So, the result of the expression \(8 - \frac{6}{5} \div 5\) is \(\frac{194}{25}\). If you want to express this as a mixed number, it is:
\[
7 \frac{19}{25}
\]
Thus, the final answer can be represented as \(\frac{194}{25}\) or \(7 \frac{19}{25}\).
1. **Calculate the division part first**:
\[
\frac{6}{5} \div 5
\]
To divide by a whole number, you can multiply by the reciprocal:
\[
\frac{6}{5} \div 5 = \frac{6}{5} \times \frac{1}{5} = \frac{6 \times 1}{5 \times 5} = \frac{6}{25}
\]
2. **Now substitute this back into the expression**:
\[
8 - \frac{6}{25}
\]
3. **Convert 8 to a fraction with a denominator of 25**:
\[
8 = \frac{8 \times 25}{1 \times 25} = \frac{200}{25}
\]
4. **Now subtract \(\frac{6}{25}\) from \(\frac{200}{25}\)**:
\[
\frac{200}{25} - \frac{6}{25} = \frac{200 - 6}{25} = \frac{194}{25}
\]
So, the result of the expression \(8 - \frac{6}{5} \div 5\) is \(\frac{194}{25}\). If you want to express this as a mixed number, it is:
\[
7 \frac{19}{25}
\]
Thus, the final answer can be represented as \(\frac{194}{25}\) or \(7 \frac{19}{25}\).
Answered by
GPT-4o mini
To evaluate the expression \(8 - \frac{6}{3} \div 5\), we will follow the order of operations (PEMDAS/BODMAS):
1. **Calculate \(\frac{6}{3}\)**:
\[
\frac{6}{3} = 2
\]
2. **Now, divide that result by 5**:
\[
2 \div 5 = \frac{2}{5}
\]
3. **Substitute this back into the expression**:
\[
8 - \frac{2}{5}
\]
4. **Convert 8 to a fraction with a denominator of 5**:
\[
8 = \frac{8 \times 5}{1 \times 5} = \frac{40}{5}
\]
5. **Now subtract \(\frac{2}{5}\) from \(\frac{40}{5}\)**:
\[
\frac{40}{5} - \frac{2}{5} = \frac{40 - 2}{5} = \frac{38}{5}
\]
So, the result of the expression \(8 - \frac{6}{3} \div 5\) is \(\frac{38}{5}\).
If you want to express this as a mixed number, it can be written as:
\[
7 \frac{3}{5}
\]
Thus, the final answer can be represented as \(\frac{38}{5}\) or \(7 \frac{3}{5}\).
1. **Calculate \(\frac{6}{3}\)**:
\[
\frac{6}{3} = 2
\]
2. **Now, divide that result by 5**:
\[
2 \div 5 = \frac{2}{5}
\]
3. **Substitute this back into the expression**:
\[
8 - \frac{2}{5}
\]
4. **Convert 8 to a fraction with a denominator of 5**:
\[
8 = \frac{8 \times 5}{1 \times 5} = \frac{40}{5}
\]
5. **Now subtract \(\frac{2}{5}\) from \(\frac{40}{5}\)**:
\[
\frac{40}{5} - \frac{2}{5} = \frac{40 - 2}{5} = \frac{38}{5}
\]
So, the result of the expression \(8 - \frac{6}{3} \div 5\) is \(\frac{38}{5}\).
If you want to express this as a mixed number, it can be written as:
\[
7 \frac{3}{5}
\]
Thus, the final answer can be represented as \(\frac{38}{5}\) or \(7 \frac{3}{5}\).
Answered by
GPT-4o mini
To find the prime factorization of \(720\), you can follow these steps:
### Step 1: Start with the number 720.
### Step 2: Divide by the smallest prime number.
1. **Divide by 2** (the smallest prime number):
\[
720 \div 2 = 360
\]
So, \(720 = 2 \times 360\)
2. **Divide 360 by 2**:
\[
360 \div 2 = 180
\]
So, \(720 = 2 \times 2 \times 180\)
3. **Divide 180 by 2**:
\[
180 \div 2 = 90
\]
So, \(720 = 2 \times 2 \times 2 \times 90\)
4. **Divide 90 by 2**:
\[
90 \div 2 = 45
\]
So, \(720 = 2 \times 2 \times 2 \times 2 \times 45\)
### Step 3: Now, we cannot divide by 2 anymore, so we move to the next prime number, which is 3.
5. **Divide 45 by 3**:
\[
45 \div 3 = 15
\]
So, \(720 = 2 \times 2 \times 2 \times 2 \times 3 \times 15\)
6. **Divide 15 by 3**:
\[
15 \div 3 = 5
\]
So, \(720 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5\)
### Step 4: Now we are left with 5, which is a prime number itself.
### Step 5: Write out the full prime factorization.
Putting all the factors together, we have:
\[
720 = 2^4 \times 3^2 \times 5^1
\]
### Conclusion:
The prime factorization of \(720\) is:
\[
2^4 \times 3^2 \times 5
\]
### Step 1: Start with the number 720.
### Step 2: Divide by the smallest prime number.
1. **Divide by 2** (the smallest prime number):
\[
720 \div 2 = 360
\]
So, \(720 = 2 \times 360\)
2. **Divide 360 by 2**:
\[
360 \div 2 = 180
\]
So, \(720 = 2 \times 2 \times 180\)
3. **Divide 180 by 2**:
\[
180 \div 2 = 90
\]
So, \(720 = 2 \times 2 \times 2 \times 90\)
4. **Divide 90 by 2**:
\[
90 \div 2 = 45
\]
So, \(720 = 2 \times 2 \times 2 \times 2 \times 45\)
### Step 3: Now, we cannot divide by 2 anymore, so we move to the next prime number, which is 3.
5. **Divide 45 by 3**:
\[
45 \div 3 = 15
\]
So, \(720 = 2 \times 2 \times 2 \times 2 \times 3 \times 15\)
6. **Divide 15 by 3**:
\[
15 \div 3 = 5
\]
So, \(720 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5\)
### Step 4: Now we are left with 5, which is a prime number itself.
### Step 5: Write out the full prime factorization.
Putting all the factors together, we have:
\[
720 = 2^4 \times 3^2 \times 5^1
\]
### Conclusion:
The prime factorization of \(720\) is:
\[
2^4 \times 3^2 \times 5
\]
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