Grade 8 math problem

Question

Find their sum. Explain the method you use. 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 2/3 + 2/4 + 2/5 + 2/6 + 3/4 + 3/5 + 3/6 + 4/5 + 4/6 + 5/6

Answer 1

 

 

 

 

1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+(1/6+2/6+3/6+4/6+5/6)=

1/2+(1+2)/3+(1+2+3)/4+(1+2+3+4)/5+(1+2+3+4+5)/6=

1/2+1+6/4+2+15/6=1/2+1+3/2+2+5/2=3+(1+3+5)/2=3+9/2=7½.

Answer 2

 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 2/3 + 2/4 + 2/5 + 2/6 + 3/4 + 3/5 + 3/6 + 4/5 + 4/6 + 5/6 =  7.5

You could use a calculater for this.

Comments

no calculator is not allowed and  i need a method to solve if there are lot of  fractions and we have to add them