Question
Part F
To divide 9/12 by 2/12, answer this question: How many sets of 2/12 are in 9/12? Use the model representing the fraction 9/12 to help you answer the question. (Hint:
Think about grouping the blue boxes into pairs.)
To divide 9/12 by 2/12, answer this question: How many sets of 2/12 are in 9/12? Use the model representing the fraction 9/12 to help you answer the question. (Hint:
Think about grouping the blue boxes into pairs.)
Answers
Answered by
GPT-4o mini
To find out how many sets of \( \frac{2}{12} \) are in \( \frac{9}{12} \), we can think of this in terms of division of fractions.
1. **Set Up the Division**:
We are essentially trying to solve the problem:
\[
\frac{9}{12} \div \frac{2}{12}
\]
2. **Convert the Division into Multiplication**:
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
\[
\frac{9}{12} \div \frac{2}{12} = \frac{9}{12} \times \frac{12}{2}
\]
3. **Perform the Multiplication**:
Now let's multiply:
\[
\frac{9 \times 12}{12 \times 2} = \frac{108}{24}
\]
4. **Simplify the Fraction**:
We can simplify \( \frac{108}{24} \) by dividing by the greatest common divisor (GCD), which is 12:
\[
\frac{108 \div 12}{24 \div 12} = \frac{9}{2} = 4.5
\]
So, there are **4.5 sets** of \( \frac{2}{12} \) in \( \frac{9}{12} \).
To visualize this, if you group the \( 9/12 \) into sets (or boxes) of \( 2/12 \):
- You would fit 4 full sets of \( 2/12 \) into \( 9/12 \), which accounts for \( 8/12 \), and then there is half a set of \( 2/12 \) remaining (which is \( 1/12 \)). Therefore, you can say that there are 4 complete sets, plus part of another set, leading to the total of 4.5 sets.
1. **Set Up the Division**:
We are essentially trying to solve the problem:
\[
\frac{9}{12} \div \frac{2}{12}
\]
2. **Convert the Division into Multiplication**:
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
\[
\frac{9}{12} \div \frac{2}{12} = \frac{9}{12} \times \frac{12}{2}
\]
3. **Perform the Multiplication**:
Now let's multiply:
\[
\frac{9 \times 12}{12 \times 2} = \frac{108}{24}
\]
4. **Simplify the Fraction**:
We can simplify \( \frac{108}{24} \) by dividing by the greatest common divisor (GCD), which is 12:
\[
\frac{108 \div 12}{24 \div 12} = \frac{9}{2} = 4.5
\]
So, there are **4.5 sets** of \( \frac{2}{12} \) in \( \frac{9}{12} \).
To visualize this, if you group the \( 9/12 \) into sets (or boxes) of \( 2/12 \):
- You would fit 4 full sets of \( 2/12 \) into \( 9/12 \), which accounts for \( 8/12 \), and then there is half a set of \( 2/12 \) remaining (which is \( 1/12 \)). Therefore, you can say that there are 4 complete sets, plus part of another set, leading to the total of 4.5 sets.