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

He ate
`(1)/(20)` of the original pizza for dinner

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
`(1)/(3)`

∴ Teddy takes
`(1)/(3)` of the pizza

- Teddy eats
`(5)/(8)` of his piece for lunch and a further
`(2)/(5)` of what

remains for dinner

∵ His piece is
`(1)/(3)`

∵ He eats
`(5)/(8)` of his piece for lunch

∴ He eats for lunch =
`(5)/(8)` ×
`(1)/(3)` =
`(5)/(24)`

- Let us find the remaining of his piece for dinner

∵ The remaining =
`(1)/(3)` -
`(5)/(24)`

- Make L.C.M for the denominators

∵ The L.C.M of 3 and 24 is 24

∵
`(1)/(3)` =
`(1*8)/(3*8)` =
`(8)/(24)`

∴ The remaining =
`(8)/(24)` -
`(5)/(24)`

∴ The remaining =
`(3)/(24)` =
`(1)/(8)`

∵ He ate
`(2)/(5)` of the remaining for dinner

∵ The remaining of his piece =
`(1)/(8)`

∴ He ate for dinner ⇒
`(2)/(5)` ×
`(1)/(8)`

∴ He ate for dinner ⇒
`(2)/(40)` =
`(1)/(20)`

* He ate
`(1)/(20)` of the original pizza for dinner