Question

Write the following expression as a fraction in lowest terms:

Answer 1

Answer:

Mixed Number Form: $4\frac{4}{9}$

(Improper Fraction Form: $\frac{40}{9}$

Step-by-step explanation:

Step 1: Simplify the other fractions

$\[2 + \cfrac{2}{2} + \cfrac{3}{3} + \cfrac{4}{4 + 5}}}\]$

$\frac{2}{2}$ can be simplified to just 1 because 2 ÷ 2 = 1

Same with $\frac{3}{3}$

Now we have:

$2+1+1+\frac{4}{4+5}$

Add all the whole numbers:

$4+\frac{4}{4+5}$

Add the whole number to make it into a mixed number, add the 2 denominators together as well:

$4\frac{4}{9}$

This is already in the simplest terms but if you want the exact term:

$\frac{40}{9}$

Answer 2

Step-by-step explanation:

$\[2 + \cfrac{2}{2 + \cfrac{3}{3 + \cfrac{4}{4 + 5}}}\]=$

$\[2 + \cfrac{2}{2 + \cfrac{3}{3 + \cfrac{4}{9}}}\]=$

$\[2 + \cfrac{2}{2 + \cfrac{3}{\cfrac{31}{9}}}\]=$

$\[2 + \cfrac{2}{2 + \cfrac{27}{31} }}}\]=$

$\[2 + \cfrac{2}{ \cfrac{62+27}{31} }}}\]=$

$\[2 + \cfrac{2}{ \cfrac{89}{31} }}}\]=$

$\[2 + \cfrac{62}{{89} }}}\]=$

$\[2 \cfrac{62}{{89} }}}\]$