Answer:
1. [tex]\sf\large{ \frac{27}{50}}[/tex]kg
2. 1.5 liters
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Given:
[tex]\sf{ \frac{8}{10}}[/tex]kg = cooked amount of spaghetti
[tex]\sf{ \frac{1}{5}}[/tex]kg = given to the neighbor
[tex]{}[/tex]
Solution:
1.) Get [tex]\sf\large{ \frac{1}{5}}[/tex] of [tex]\sf{ \frac{8}{10}}[/tex]
[tex]\sf\large{ \frac{1}{5} × \frac{8}{10}\:=\: \frac{1}{5} × \frac{4 × \cancel{2}}{5 × \cancel{2}}}[/tex]
= [tex]\sf\large{ \frac{1}{5} × \frac{4}{5}}[/tex]
= [tex]\sf\large{ \frac{4}{25}}[/tex] since [tex]\sf\large{\frac{A}{B} × \frac{C}{D} = \frac{AC}{BD}}[/tex]
Now, the remaining amount of spaghetti is computed as follows:
[tex]\sf\large{ \frac{8}{10} - \frac{4}{25} = \frac{4 × 2}{5 × 2} - \frac{4}{25}}[/tex]
= [tex]\sf\large{ \frac{4}{5} - \frac{4}{25}}[/tex]
= [tex]\sf\large{ \frac{4 × 5}{5 × 5} - \frac{4}{25}}[/tex]
= [tex]\sf\large{ \frac{20}{25} - \frac{4}{25}}[/tex]
= [tex]\sf\large{ \frac{16}{25}}[/tex]kg because [tex]\sf\large{ \frac{A}{C} ± \frac{B}{C} = \frac{A ± B}{C}}[/tex]
Now, to find the amount of what they have eaten,
Subtract the remaining [tex]\sf\large{ \frac{16}{25}}[/tex]kg by [tex]\sf\large{ \frac{1}{10}}[/tex]kg
[tex]\sf\large{ \frac{16}{25} - \frac{1}{10} = \frac{16 × 2}{25 × 2} - \frac{1 × 5}{10 × 5}}[/tex]
= [tex]\sf\large{ \frac{32}{50} - \frac{5}{50}}[/tex]
= [tex]\sf\large{ \frac{27}{50}}[/tex]kg
Thus, the mother and her children ate [tex]\sf{ \frac{27}{50}}[/tex]kg of spaghetti.
Answer: [tex]\sf\large{ \frac{27}{50}}[/tex]kg
[tex]{}[/tex]
2.) [tex]\sf\large{ \frac{5}{6} + \frac{8}{12} = \frac{5 × 2 + 8}{12} = \frac{10 + 8}{12} = \frac{18}{12} = \frac{18 ÷ 6}{12 ÷ 6} = \frac{3}{2} = 1.5\:liters}[/tex]
Answer: 1.5 liters
