Ann-Emily, 2nd grader, adds fractions using complex fractions and multiplies mixed numbers-WOW!

Don gave Ann-Emily the problem 2/3 + 1/4 = ? He walked away to work with other students. When he came back, he saw this picture (without 1/8 and so on in black print which he put in after to help him and other people understand what she did).

Ann-Emily explained the picture to Don (as he remembered it): The whole is a 12x12 square. The red section is 2/3 of that. The blue part is 1/4 of it.

The 3 vertical rows at the left, make up 1/4 of the whole. Half of 1/4 is 1/8. So she counted 4/8 for the 4 sections. Looking at the 2 red vertical rows to the right, that was 2/3/8 (2/3 of an 8th) on top and 2/3/8 on the bottom. Ann-Emily added the 1/8's to get the red total: 1/8 + 1/8 + 1/8 + 1/8 + 2/3/8 + 2/3/8 = 4/8 + 4/3/8 = 4/8 + 1 1/3/8 =
5 1/3/8 ([5 and 1/3] eighths). The blue section is 1/4 = 2/8, so the total 2/3 + 1/4 = 7 1/3/8 (on the right above), which was her answer. Don was really impressed with Ann-Emily's use of complex fractions. He checked her answer for himself, by changing the complex fraction to a simple fraction by multiplying top and bottom by 3 to get 22/24 = 11/12. Then he looked at her picture and got 11/12 also.

Ann-Emily multiplies 3 1/2 x 2 1/3

See her picture below: First she did 3 1/2 x 2 = 7, then 3 x 1/3 = 1, then 1/2 x 1/3 = 1/6, then added these to get 8 1/6. Simple!

Fine job Ann-Emily!

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