A man spent 5/12of his income on food and 1/7 of the reminder on books . what fractions of his income was left for other expenses
1 - 5/12 - 1/7 * 7/12 = 1/2
Well, it seems like this man had quite an appetite for food and knowledge! Let me do a bit of math to find out how much of his income was left for other expenses.
If he spent 5/12 of his income on food, it means he had 7/12 remaining.
Then, if he spent 1/7 of that reminder on books, we can multiply 7/12 by 1/7 to find out how much was spent on books. That gives us 1/12.
So, if 1/12 of his income was spent on books, that means he still had 11/12 (since 1 - 1/12 = 11/12) of his income left for other expenses.
Looks like this man still has a pretty decent chunk of his income to spend on some good ol' clown shoes or whatever else catches his fancy!
To solve this problem, let's break it down step by step:
Step 1: The man spent 5/12 of his income on food.
Step 2: This means that 12/12 - 5/12 = 7/12 of his income is left after spending on food.
Step 3: From the remaining 7/12, he spends 1/7 on books.
Step 4: To find out how much is left for other expenses, we subtract 1/7 from 7/12.
Step 5: Let's find a common denominator for 12 and 7, which is 84.
Step 6: Multiply the numerator and denominator of 7/12 by 7 to have the same denominator as 7/84.
Step 7: Multiply the numerator and denominator of 1/7 by 12 to have the same denominator as 12/84.
Step 8: Now, we can subtract 12/84 - 7/84 = 5/84
Step 9: Therefore, 5/84 of his income is left for other expenses.
So, the fraction of his income left for other expenses is 5/84.
To find the fraction of the man's income that was left for other expenses, we first need to calculate the amount he spent on food and books.
Let's say the man's income is represented by the fraction 1.
The fraction of his income that he spent on food is 5/12. So, the amount spent on food can be calculated as (5/12) * 1 = 5/12.
Now, we need to calculate the remainder after the food expense. To do that, we subtract the food expense from the total income:
Remaining income = 1 - 5/12 = 12/12 - 5/12 = 7/12.
The fraction of the remaining income that he spent on books is 1/7. So, the amount spent on books can be calculated as (1/7) * (7/12) = 1/12.
Now, we subtract the book expense from the remaining income:
Remaining income = 7/12 - 1/12 = 6/12 = 1/2.
Therefore, the fraction of the man's income that was left for other expenses is 1/2.