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3

The student was conflating the sum $$\frac45+\frac23$$ and the weighted average (where the weights account for group-size differences) $$\left(\frac{\color{#00F}5}{\color{#180}{5+3}}\right)\frac45+\left(\frac{\color{#00F}3}{\color{#180}{5+3}}\right)\frac23\\=\frac{4+2}{5+3}$$ of the two given fractions/rates. Clearly, the sum of two positive fractions is ...


8

The student who designed this problem wasn't thinking about the different wholes. IN your students problem, there are 3 different wholes. Anna's flowers - The whole is 5 flowers and $\frac{4}{5}$ are daffodils Beatrice's flowers The whole is 3 flowers and $\frac{2}{3}$ are daffodils The flowers of Anna and Beatrice combined. The whold is 8 flowers and $\...


2

What property of fractions or addition of fractions could they be misunderstanding, and how would you explain to the student where they have gone wrong so that they don't repeat this in the future? [Emphasis added.] Short Answer Fractions are numbers and they behave like numbers when we do operations on them. Many students never learn this. You (and the ...


7

The word you are looking for is mediant. The mediant of two fractions $\frac{a}{c}$ and $\frac{b}{d}$ is $\frac{a+b}{c+d}$. According to Wikipedia, It is sometimes called the freshman sum, as it is a common mistake in the early stages of learning about addition of fractions. Teachers often do this in grading papers. For example, a test has two parts: the ...


1

I remember getting my first 18 inch slide ruler. I had worked hard, poison oak filled, hours making fire breaks in the Oakland hills to make enough money to get it. It was aluminum, had a spring loaded cursor that slid like it was greased, and the C and D scales (I think) lined up perfectly. It was huge and had scales I was never going to use. I loved it. ...


8

It sounds like a variation of subtracting that I learned in high school (1968). My instructor called it European subtraction. \begin{array}{ccc} & 3 & 4 & 2 \\ - & 1 & 7 & 3 \\ \hline \end{array} You start by saying $9$ plus $3$ is $12$. You write the $9$ as shown and "carry" the $1$, of the $12$, as a subscript of the $7$ ...


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