Don to Maya: Try this problem 2 1/2 + 4 1/4
Maya: Well 2+4=6 , then she draws a picture showing 1/2 + 1/4 = 3/4 and says
Don: That looks fine.
Maya: How do you make a fraction like 1/2 on the calculator?
Don shows Maya: He presses the 1 key, then the ' key, then the 2 key and the calculator shows 1/2 on the screen.
Don: This shows that the fraction ' means 1 divided by 2 (among other things!)
Maya: Puts in the calculator 2 + 1/2 + 4 + 1/4 and presses ENTER; the calculator shows the answer as 6.75 on the screen, not 6 3/4
Don: Well you know that 75 cents = 0.75 = ' of a dollar, so 6.75 = 6 3/4 , which is what you had.
Don: let me show you how the calculator changes 6.75 to a fraction!
Don: types in 6.75, presses MATH, NUM, >fraction, enter, and calculator gives 27/4
Don: what is this? Is this 6 3/4 ?
Maya: I don't know.
Don: Well you know 1= 4/4 , 2= 8/4, 3=12/4,
Maya: .. and 4 =16/4, 5 =20/4, 6= 24/4. So 24/4 + 3/4 = 27/4 = 6 3/4
Maya: Why does the calculator give the answer 6.75 and 27/4 and not 6 3/4?
Don: We can write 6 3/4 lots of ways. Whoever made the calculator, had it only write it as 6.75 and 27/4.
Maya: Can I show this to Mommy?
Don: first explain what we just did to me.. what did we start with?... then she ran upstairs to show her Mom.
Later Don put 2 + 1/2 + 4 + 1/4 into WolframAlpha, which gave the following 5 results:
Exact answer: 27/4
Decimal form: 6.75
Mixed fraction: 6 '
Prime factorization: 2-2 x 33
Egyptian fraction expansion: 6 + ' + '
At their next meeting a week later, Don went over these results with Maya.