The fraction of his lotto earnings that is remaining is 7/20.
What is a fraction?
A fraction is a portion of a whole or, more broadly, a set of equal pieces.
Let the total amount that the man won in the lotto jackpot is x.
Now, he spent 2/5 of the jackpot on luxury cars and 1/4 on buying a house, therefore, the total spending he will do is,
[tex]\dfrac{2x}{5}+\dfrac{x}{4}[/tex]
Now, the fraction of his lotto earnings that is remaining can be written as,
[tex]x-\dfrac{2x}{5}+\dfrac{x}{4}\\\\\\=\dfrac{x}{1}-\dfrac{2x}{5}-\dfrac{x}{4}\\\\\\=\dfrac{x \times 20}{1 \times 20}-\dfrac{2x \times 4}{5 \times 4}-\dfrac{x\times 5}{4\times 5}\\\\\\=\dfrac{20x-8x-5x}{20}\\\\=\dfrac{7x}{20}[/tex]
Hence, the fraction of his lotto earnings that is remaining is 7/20.
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