… I don't fully understand … the equations … in the highlighted box …
Hi bobisaka. They've substituted each value for n, directly
above the highlighted box. Next, they
evaluate those expressions (that is, they
do the arithmetic). The evaluation steps are shown inside the highlighted box.
The order of operations tells us to do multiplications before subtractions. Therefore, the first line inside the box shows the results of the multiplications:
In the left column, they multiplied 5·\(\frac{2}{5}\) to get 2, and they multiplied 6·\(\frac{2}{5}\) to get 12/5.
In the right column, they multiplied 5·\(\frac{1}{6}\) to get 5/6, and they multiplied 6·\(\frac{1}{6}\) to get 1.
The second line inside the box shows the results of the subtractions:
In the left column, 2 - 2 is 0, and \(\frac{12}{5}-\frac{5}{5}\) is \(\frac{7}{5}\).
In the right column, \(\frac{5}{6}-\frac{12}{6}\) is \(\frac{-7}{6}\), and 1 - 1 is 0.
Multiplying any amount by zero results in zero; therefore, in each case, the substituted value of n results in the statement 0=0 -- which is true. That completes the check.
Does this answer your question, or were you thinking about something else?
?