Question

lucas divides his pizza into three equal pieces for himself and his two friends. his friend teddy eats 5/8 of his piece for lunch and a further 2/5 of what remains for dinner. what fraction of the original pizza did teddy eat for dinner

Answer 1

Answer:

He ate $\frac{1}{20}$ 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 $\frac{1}{3}$

∴ Teddy takes $\frac{1}{3}$ of the pizza

- Teddy eats $\frac{5}{8}$ of his piece for lunch and a further $\frac{2}{5}$ of what

  remains for dinner

∵ His piece is $\frac{1}{3}$

∵ He eats $\frac{5}{8}$ of his piece for lunch

∴ He eats for lunch = $\frac{5}{8}$ × $\frac{1}{3}$ = $\frac{5}{24}$

- Let us find the remaining of his piece for dinner

∵ The remaining = $\frac{1}{3}$ - $\frac{5}{24}$

- Make L.C.M for the denominators

∵ The L.C.M of 3 and 24 is 24

∵ $\frac{1}{3}$ = $\frac{1*8}{3*8}$ = $\frac{8}{24}$

∴ The remaining = $\frac{8}{24}$ - $\frac{5}{24}$

∴ The remaining = $\frac{3}{24}$ = $\frac{1}{8}$

∵ He ate $\frac{2}{5}$ of the remaining for dinner

∵ The remaining of his piece = $\frac{1}{8}$

∴ He ate for dinner ⇒ $\frac{2}{5}$ × $\frac{1}{8}$

∴ He ate for dinner ⇒ $\frac{2}{40}$ = $\frac{1}{20}$

* He ate $\frac{1}{20}$ of the original pizza for dinner