Answer:
He ate [tex]\frac{1}{20}[/tex] of the original pizza for dinner
Step-by-step explanation:
- Lucas divides his pizza into three equal pieces for himself and his two
friends
∵ There are 1 pizza
∵ It is divided into 3 equal parts
∴ Each part is [tex]\frac{1}{3}[/tex]
∴ Teddy takes [tex]\frac{1}{3}[/tex] of the pizza
- Teddy eats [tex]\frac{5}{8}[/tex] of his piece for lunch and a further [tex]\frac{2}{5}[/tex] of what
remains for dinner
∵ His piece is [tex]\frac{1}{3}[/tex]
∵ He eats [tex]\frac{5}{8}[/tex] of his piece for lunch
∴ He eats for lunch = [tex]\frac{5}{8}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{5}{24}[/tex]
- Let us find the remaining of his piece for dinner
∵ The remaining = [tex]\frac{1}{3}[/tex] - [tex]\frac{5}{24}[/tex]
- Make L.C.M for the denominators
∵ The L.C.M of 3 and 24 is 24
∵ [tex]\frac{1}{3}[/tex] = [tex]\frac{1*8}{3*8}[/tex] = [tex]\frac{8}{24}[/tex]
∴ The remaining = [tex]\frac{8}{24}[/tex] - [tex]\frac{5}{24}[/tex]
∴ The remaining = [tex]\frac{3}{24}[/tex] = [tex]\frac{1}{8}[/tex]
∵ He ate [tex]\frac{2}{5}[/tex] of the remaining for dinner
∵ The remaining of his piece = [tex]\frac{1}{8}[/tex]
∴ He ate for dinner ⇒ [tex]\frac{2}{5}[/tex] × [tex]\frac{1}{8}[/tex]
∴ He ate for dinner ⇒ [tex]\frac{2}{40}[/tex] = [tex]\frac{1}{20}[/tex]
* He ate [tex]\frac{1}{20}[/tex] of the original pizza for dinner
