six people ate one tenth of a pie and there was two fifth left. How much pie did she start with?
6 * 1/10 = 6/10 = 3/5
3/5 + 2/5 = 5/5 = 1
To find out how much pie she started with, we can work backwards from the information given. Let's break down the problem step by step:
Step 1: Determine how much pie remains.
It is stated that two-fifths of the pie was left. So, if two-fifths were left, it means that three-fifths (5/5 - 2/5) of the pie was eaten.
Step 2: Calculate the fraction of the pie that was eaten.
If three-fifths of the pie was eaten and six people shared it equally, each person would have eaten one-sixth (3/5 ÷ 6) of the pie.
Step 3: Calculate the fraction of the pie that was not eaten.
Since each person ate one-tenth of the pie, there were 10 parts in total. So, the remaining portion that was not eaten can be represented as (10 - 1) or nine-tenths (9/10) of the pie.
Step 4: Calculate the whole pie.
Since nine-tenths of the pie was left and this represents the total pie, we can set up the equation: 9/10 = 1 whole pie.
Step 5: Solve the equation.
To solve for the whole pie, we need to find the value of one whole pie when nine-tenths equals one pie. We can do this by multiplying both sides of the equation by 10/9 (the reciprocal of 9/10): 9/10 * 10/9 = 1 * 10/9. This simplifies to 1 = 10/9.
So, the whole pie can be represented by 10/9.
However, since it's unusual to have a fraction greater than one to represent a whole pie, we can convert the fraction to a mixed number. One whole pie would be equal to 1 and 1/9.
Therefore, she started with 1 and 1/9 of the pie.