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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.)

1 answer

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.