Can you find three different fractional units that add up to 1? It turns Class 6

Can you find three different fractional units that add up to 1? It turns Class 6

Question 1.

Can you find three different fractional units that add up to 1? It turns out there is only one solution to this problem (up to changing the order of the 3 fractions)! Can you find it? Try to find it before reading further. Class 6

Solution:

[latex]\frac{1}{2}[/latex] + [latex]\frac{1}{3}[/latex] + [latex]\frac{1}{6}[/latex] = 1.

Question 2.

Can you find four different fractional units that add up to 1? It turns out that this problem has six solutions! Can you find at least one of them? Can you find them all? Class 6

You can try using similar reasoning as in the cases of two and three fractional units — or find your own method!

Solution:

One solution is as shown below :

[latex]\frac{1}{2}[/latex] + [latex]\frac{1}{4}[/latex] + [latex]\frac{1}{6}[/latex] + [latex]\frac{1}{12}[/latex] = 1.

Because, [latex]\frac{1}{2}[/latex] + [latex]\frac{1}{4}[/latex] + [latex]\frac{1}{6}[/latex] + [latex]\frac{1}{12}[/latex] = [latex]\frac{6+3+2+1}{12}[/latex]

= [latex]\frac{12}{2}[/latex] = 1

It can be shown in a circle as given below :

The remaining five solutions are as shown below :

(i) $1=\frac{1}{2}+\frac{1}{3}+\frac{1}{9}+\frac{1}{18}$

(ii) $1=\frac{1}{2}+\frac{1}{3}+\frac{1}{8}+\frac{1}{24}$

(iii) $1=\frac{1}{2}+\frac{1}{4}+\frac{1}{5}+\frac{1}{20}$

(iv) $1=\frac{1}{2}+\frac{1}{3}+\frac{1}{10}+\frac{1}{15}$

(v) $1=\frac{1}{2}+\frac{1}{3}+\frac{1}{7}+\frac{1}{42}$