Question
Solve the division problem shown in the picture. %0D%0A%0D%0A%0D%0ABe sure to use KEEP, CHANGE, FLIP!%0D%0A%0D%0A%0D%0ASimplify your answer if possible. %0D%0A%0D%0A%0D%0AA.%0D%0A-24/55%0D%0A%0D%0AB.%0D%0A-15/22%0D%0A%0D%0AC.%0D%0A24/55%0D%0A%0D%0AD.%0D%0A15/22
Answers
GPT-4o mini
To solve a division problem involving fractions using the "KEEP, CHANGE, FLIP" method, let's consider the division of two fractions \( \frac{a}{b} \div \frac{c}{d} \):
1. **Keep** the first fraction as it is: \( \frac{a}{b} \)
2. **Change** the division sign to multiplication: \( \times \)
3. **Flip** the second fraction by taking its reciprocal: \( \frac{d}{c} \)
Therefore, the division problem can be rewritten as:
\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
\]
Now, let's apply this to a specific example. If we are dividing \( \frac{-24}{55} \) by \( \frac{-15}{22} \), we would follow these steps:
1. **Keep**: \( \frac{-24}{55} \)
2. **Change**: from division to multiplication, giving us \( \times \)
3. **Flip**: the second fraction \( \frac{-15}{22} \) to \( \frac{22}{-15} \)
This gives us:
\[
\frac{-24}{55} \div \frac{-15}{22} = \frac{-24}{55} \times \frac{22}{-15}
\]
Now we multiply the numerators and the denominators:
\[
\frac{-24 \times 22}{55 \times -15}
\]
The negatives cancel out:
\[
\frac{24 \times 22}{55 \times 15}
\]
Now, we need to simplify this expression. Calculating the numbers:
- \( 24 \times 22 = 528 \)
- \( 55 \times 15 = 825 \)
Thus, we have:
\[
\frac{528}{825}
\]
Next, we can simplify this fraction by finding the greatest common divisor (GCD) of 528 and 825. The GCD is 33.
Now we can reduce the fraction:
\[
\frac{528 \div 33}{825 \div 33} = \frac{16}{25}
\]
So, the final answer is:
\[
\frac{16}{25}
\]
None of the answer choices you provided match this final result. If you have more context or a specific problem statement, please share, and I can assist you further!
1. **Keep** the first fraction as it is: \( \frac{a}{b} \)
2. **Change** the division sign to multiplication: \( \times \)
3. **Flip** the second fraction by taking its reciprocal: \( \frac{d}{c} \)
Therefore, the division problem can be rewritten as:
\[
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
\]
Now, let's apply this to a specific example. If we are dividing \( \frac{-24}{55} \) by \( \frac{-15}{22} \), we would follow these steps:
1. **Keep**: \( \frac{-24}{55} \)
2. **Change**: from division to multiplication, giving us \( \times \)
3. **Flip**: the second fraction \( \frac{-15}{22} \) to \( \frac{22}{-15} \)
This gives us:
\[
\frac{-24}{55} \div \frac{-15}{22} = \frac{-24}{55} \times \frac{22}{-15}
\]
Now we multiply the numerators and the denominators:
\[
\frac{-24 \times 22}{55 \times -15}
\]
The negatives cancel out:
\[
\frac{24 \times 22}{55 \times 15}
\]
Now, we need to simplify this expression. Calculating the numbers:
- \( 24 \times 22 = 528 \)
- \( 55 \times 15 = 825 \)
Thus, we have:
\[
\frac{528}{825}
\]
Next, we can simplify this fraction by finding the greatest common divisor (GCD) of 528 and 825. The GCD is 33.
Now we can reduce the fraction:
\[
\frac{528 \div 33}{825 \div 33} = \frac{16}{25}
\]
So, the final answer is:
\[
\frac{16}{25}
\]
None of the answer choices you provided match this final result. If you have more context or a specific problem statement, please share, and I can assist you further!