To subtract the fractions, we should make them all share a common denominator. We can either multiply the fractions by the opposite denominator, or find a much smaller common denominator. In this case, we should find the multiples of 6 and 9:
Multiples of 6: 6, 12, 18, 24, 30... 6 · 3 = 18
Multiples of 9: 9, 18, 27, 36, 45... 9 · 2 = 18
Notice how the least common denominator is 18.
Remember that whatever you to do the bottom, you must also do to the top. Starting with [tex]\frac{1}{6}[/tex]:
[tex]\frac{1}{6}[/tex] · [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{18}[/tex]
Now the [tex]\frac{4}{9}[/tex]:
[tex]\frac{4}{9}[/tex] · [tex]\frac{2}{2}[/tex] = [tex]\frac{8}{18}[/tex]
Now, we can rewrite the equation as:
2 [tex]\frac{3}{18}[/tex] - 3 [tex]\frac{8}{18}[/tex]
2 - 3 = -1
[tex]\frac{3}{18}[/tex] - [tex]\frac{8}{18}[/tex] = [tex]\frac{-5}{18}[/tex]
Therefore, 2 [tex]\frac{1}{6}[/tex] - 3 [tex]\frac{4}{9}[/tex] = -1 [tex]\frac{5}{18}[/tex].
Hope this helps! :)
