Anna said that the product of 78⋅112=7278·112=72. How can you tell that her answer is wrong?

The easiest way I can think of to show someone who is not very mathematically inclined that the calculation is wrong (other than using a scientific calculator) is this:

Explain that one half contains four eighths - you can visualize this very simply with a pie chart.

Then tell Anna that mathematically speaking this translates to the equation:

1/2 = 4 * 1/8

Now, if ONE half is equal to four times ONE eighths, then SEVEN halves is equal to four times SEVEN eighths - basically, you just multiply both sides by 7:

7/2 = 4 * 7/8

Now, compare this to the equation proposed by Anna:

7/2 = 1½ * 7/8

I guess, at this point it will be easy to convince Anna that 1½ is not 4, and therefore her equation is faulty.

Alternatively, if she's sound with fractions you could also tell her that to get from 7/8 to 7/2 you will need a factor which only affects the denominator as the numerator stay the same. The factor that turns 8 into 2 is 1/4 but since this takes place in the denominator we need the reciprocal to turn 1/8 into 1/2 - and the reciprocal of 1/4 is of course 4. At which point we've arrived at the same place of argumentation as before (which is that 4 ≠ 1½).

Step-by-step explanation:

hope this helps        :)

squares, rhombus, rectangles