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Jon has painted 4/5 of his house. The next day he painted 2/3 of what he had left. What fraction of the house is left to paint?

Respuesta :

frika

Jon has painted 4/5 of his house at the first day. Then

[tex] 1-\dfrac{4}{5} =\dfrac{5}{5} -\dfrac{4}{5} =\dfrac{1}{5}[/tex]

left.

The next day he painted 2/3 of what he had left. This is exactly 2/3 from 1/5. Mathematically you should multiply these two fractions:

[tex] \dfrac{2}{3}\cdot \dfrac{1}{5} =\dfrac{2\cdot 1}{3\cdot 5} =\dfrac{2}{15}[/tex]

he has painted the second day.

Now count how much he has painted at first and second days:

[tex] \dfrac{4}{5}+\dfrac{2}{15}=\dfrac{4\cdot 3+2}{15}=\dfrac{14}{15} . [/tex]

Then he has to paint

[tex] 1-\dfrac{14}{15} =\dfrac{15}{15}-\dfrac{14}{15}=\dfrac{1}{15} .[/tex]

Answer: [tex] \dfrac{1}{15} .[/tex]

Answer:

[tex]\displaystyle\frac{1}{15}\text{ fraction of the house is left to paint.}[/tex]

Step-by-step explanation:

We are given the following information in the question:

Amount of house painted by John = [tex]\displaystyle\frac{4}{5}[/tex]

House left to be painted =

[tex]1-\displaystyle\frac{4}{5} = \frac{1}{2}[/tex]

The next day he painted 2/3 of what was left.

House painted next day =

[tex]\displaystyle\frac{1}{5}\times \frac{2}{3} = \frac{2}{15}[/tex]

Fraction of the house is left to paint =

[tex]1 - \displaystyle\frac{4}{5}-\frac{2}{15} = \frac{15-12-2}{15} = \frac{1}{15}[/tex]

[tex]\displaystyle\frac{1}{15}\text{ \bold{fraction of the house is left to paint.}}[/tex]

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