Swarna gave 1/4 of her pocket money to her brother. Out of the remaining money she spent 1/3 for buying a book and 1/6 for watching a movie. She donated the rest of the money for charity. What fraction of her pocket money did she donate?
suppose she had an original amount of x
after giving to her brother she has 3x/4 left
of that she spends (1/3)(3x/4) and (1/6)(3x/4)
or
(1/4)x + (1/8)x
total amount spent = x/4 + x/4 + x/8 = (5/8)x
so she has 3/8 of her money left, which she donated.
check:
suppose she has 24 units of money
gave 1/4 or 6 to her brother.
She has 18 left
she spent 1/3 of that on books --- 6 units
she spent 1/6 of that on movie --- 3
amount spent = 6+6+3 = 15
amount given to charity = 24-15 = 9
Is (3/8)of 24 = 9 ??? YES
To find the fraction of Swarna's pocket money that she donated, we need to subtract the fractions she spent from 1 (the whole).
Step 1: Swarna gave 1/4 of her pocket money to her brother.
Remaining money = 1 - 1/4 = 3/4
Step 2: Out of the remaining money, she spent 1/3 for buying a book.
Remaining money after buying the book = 3/4 - 1/3
To subtract fractions with different denominators, we need to find a common denominator.
Step 3: Find a common denominator for 4 and 3, which is 12.
3/4 = (3/4) * (3/3) = 9/12
1/3 = (1/3) * (4/4) = 4/12
Subtract the fractions: 9/12 - 4/12 = 5/12
So, Swarna had 5/12 of her pocket money left after buying the book.
Step 4: Out of the remaining money, she spent 1/6 for watching a movie.
Remaining money after watching the movie = 5/12 - 1/6
Again, find a common denominator:
5/12 = (5/12) * (1/1) = 5/12
1/6 = (1/6) * (2/2) = 2/12
Subtract the fractions: 5/12 - 2/12 = 3/12
So, Swarna had 3/12 (which can be simplified to 1/4) of her pocket money left after watching the movie.
Step 5: Finally, Swarna donated the remaining money for charity.
The fraction of her pocket money that she donated is 1/4.
Therefore, Swarna donated 1/4 of her pocket money.
To find the fraction of Swarna's pocket money that she donated, we need to calculate the portion of money that she spent on buying a book and watching a movie. Since she gave 1/4 of her pocket money to her brother, she was left with 3/4 of her pocket money.
Next, let's calculate the portion of her remaining money that she spent on buying a book. Swarna spent 1/3 of her remaining money on buying the book. To find the portion of her money that she spent on buying a book, we can multiply 3/4 by 1/3:
(3/4) * (1/3) = 3/12 = 1/4
So, she spent 1/4 of her original pocket money on buying the book.
Next, let's calculate the portion of her remaining money that she spent on watching a movie. Swarna spent 1/6 of her remaining money on watching the movie. To find the portion of her money that she spent on watching a movie, we can multiply 3/4 by 1/6:
(3/4) * (1/6) = 3/24 = 1/8
So, she spent 1/8 of her original pocket money on watching the movie.
Now, let's calculate the portion of her money that she donated to charity. To find this, we need to subtract the portions she spent on buying the book and watching the movie from her original pocket money:
1 - (1/4 + 1/8) = 1 - (2/8 + 1/8) = 1 - 3/8 = 5/8
Therefore, Swarna donated 5/8 of her pocket money to charity.