Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three? Tell a story that could describe each situation.
for the same reason that 2/7 is not the same as 7/2
division is not commutative
To understand why the quotient of three divided by one-fifth is different from the quotient of one-fifth divided by three, let's imagine a story to represent each situation.
Story 1: The Quotient of Three Divided by One-fifth
Once upon a time, there were three friends - Alice, Bob, and Charlie. They decided to share a pizza among themselves. Each person should get an equal portion. So, Alice cut the pizza into five equal slices. Now the friends have five equally sized pizza slices. As they planned to divide the pizza equally, each of them would get one slice. Therefore, the quotient of three divided by one-fifth is equal to three whole pizzas.
Story 2: The Quotient of One-fifth Divided by Three
In another town, there were three friends named Sarah, Tom, and Emily. One day, they decided to bake cookies using a unique recipe. This recipe required one cup of flour. However, Sarah, Tom, and Emily had only one-fifth cup of flour available. They needed more flour, so they decided to divide the one-fifth cup into three portions equally. Each friend would get one-third (1/3) of a fifth cup of flour. Unfortunately, this tiny amount was not enough to make any cookies. Therefore, the quotient of one-fifth divided by three is equal to zero cookies.
So, in summary, the quotient of three divided by one-fifth is three whole pizzas, while the quotient of one-fifth divided by three is zero cookies. The difference arises because the order of division changes the meaning and outcome of the division operation.
Once upon a time, there were two friends named Tom and Jerry. They were both very enthusiastic about learning mathematics. One day, they came across the concept of division and decided to explore it further.
Tom, the enthusiastic and curious one, came up with a question. He wondered, "What happens when we divide three by one-fifth?" Jerry, being equally inquisitive, thought of a similar question, "And what about dividing one-fifth by three?"
Intrigued, they decided to find out the answers themselves. They started by dividing three by one-fifth. As they went through the process, they realized that dividing three by one-fifth means finding how many times one-fifth can fit into three. They measured it out and discovered that one-fifth could fit into three, a total of fifteen times.
Excitedly, Tom and Jerry came up with a story to explain their findings. They imagined a treasure chest with three gold coins inside. In their story, there were fifteen friends who wanted to share the treasure equally among themselves. So, they divided the three gold coins into fifteen equal shares, ensuring that each friend received one-fifth of a gold coin.
Moving on to the second question, Tom and Jerry attempted to divide one-fifth by three. They realized that this time, they were finding out how many times three can fit into one-fifth. They carefully calculated and found that three could not fit evenly into one-fifth, leaving them with a fraction as the answer.
With their creative storytelling minds at work, Tom and Jerry came up with another tale to explain the situation. They imagined a shy little squirrel named Sandy who had only one-fifth of a tasty acorn left. Sandy wanted to share this acorn with her three best squirrel friends. However, since the acorn was small, there wasn't enough for each squirrel to have an equal portion. In this story, they depicted the fraction as the result of dividing one-fifth by three.
Thus, Tom and Jerry discovered that the quotient of three divided by one-fifth was different from the quotient of one-fifth divided by three. One situation resulted in a whole number, indicating a perfect division, while the other situation resulted in a fraction, suggesting an unequal distribution.