# to find the sum of   2 1/2 + 4 1/4

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

2 + 1/2 + 4 + 1/4 = 6 3/4

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:

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.

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