Name: laura

Who is asking: Parent
Level: Middle

Question:
write 1/2 as the sum of ten different unit fractions. thanks



Hi Laura,

1/2 as a sum of two unit fractions is easy:

 1/2 = 1/3 +  1/6.

You will be able to extend this to a sum of ten unit fractions, noting that the last denominator is always even:

 1/6 = ( 1/2)x( 1/3) = ( 1/3 +  1/6)x( 1/3) =  1/9 +  1/18,

so that

 1/2 =  1/3 +  1/6

=  1/3 +  1/9 +  1/18.

Again we have

 1/18 = ( 1/2)x( 1/9) = ( 1/3 +  1/9 +  1/18)x( 1/9)

=  1/27 +  1/81 +  1/162,

so that

 1/2 =  1/3 +  1/9 +  1/18

=  1/3 +  1/9 +  1/27 +  1/81 +  1/162.

Continuing in this way, you will write 1/2 as a sum of 10 different unit fractions. (Looking at the pattern in the denominators can you guess the correct answer?)

Cheers,
Claude
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