Final answer:
Maya has 2/15 of her apple pie left after giving 1/6 to her friend and keeping 7/10 for herself, which were added together and then subtracted from the whole to find the remaining portion.
Step-by-step explanation:
To find out what fraction of her apple pie Maya has left after giving some away, we need to calculate the total fraction given away and subtract it from the whole pie, which is represented by the fraction 1. Maya gave 1/6 of the pie to a friend and kept 7/10 of it for herself. First, we need these fractions to have a common denominator so that we can add them together easily.
Let’s find the least common multiple (LCM) of 6 and 10, which is 30. Converting both fractions to have the denominator of 30 gives us:
- 1/6 = 5/30 (since 1×6=6 and 5×6=30)
- 7/10 = 21/30 (since 7×3=21 and 10×3=30)
Now we can add these two fractions:
5/30 (given to a friend) + 21/30 (kept by Maya) = 26/30
This means Maya has given away or used 26/30 of the pie. To find out how much of the pie is left, subtract this fraction from the whole pie (30/30):
30/30 - 26/30 = 4/30
However, this fraction can be simplified by dividing both the numerator and the denominator by the greatest common divisor (GCD), which is 2. So, the simplified answer is:
4/30 ÷ 2/2 = 2/15
Maya has 2/15 of her apple pie left.