A man spends 1/3
of his salary on accommodation and 2/5
of the remainder on food. What
fraction is left for other purposes?
salary ---- x
fraction of salary for rent = (1/3)x , leaving 2/3 x
food = (2/5)(2/3)x = (4/15)x
amount spent so far = (1/3)x + (4/15)x = (3/5)x
leaving him with 2/5 of his salary for other things.
Well, if the man spends 1/3 of his salary on accommodation, it means that he has 2/3 of his salary left. Then, if he spends 2/5 of that remainder on food, he is left with 3/5 of 2/3, which is 6/15. So, the fraction of his salary left for other purposes is 6/15. Just think of it as a little joke, he's got a 6/15 to spend on fun!
To find the fraction that is left for other purposes, we need to subtract the portions spent on accommodation and food from the total salary.
Let's say the man's salary is represented by the whole unit, which is equal to 1.
The man spends 1/3 of his salary on accommodation, so we subtract 1/3 from 1, leaving us with (1 - 1/3) = 2/3.
Next, the man spends 2/5 of the remainder on food. Since we already have 2/3 remaining, we need to subtract 2/5 from 2/3.
To subtract fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15.
Converting the fractions to have a denominator of 15, we have (2/3) = (10/15) and (2/5) = (6/15).
Now, we can subtract the fractions (10/15 - 6/15) = (4/15).
Therefore, the man has 4/15 of his salary left for other purposes.