Question

George weeded 1/5 of the garden and Summer weeded some to when they were finished 2/3 of the garden still needed to be weeded.What fraction of the garden did summer weed?

Answer 1

Let's start by subtracting the fraction of the garden that George weeded from the whole garden to find the fraction that was left for Summer to weed:

1 - 1/5 = 4/5

This tells us that 4/5 of the garden still needed to be weeded when George and Summer finished working on it.

We're told that Summer weeded some of the garden, and that the two of them together left 2/3 of the garden still needing to be weeded. We can set up an equation to represent this:

fraction George weeded + fraction Summer weeded = fraction of garden still needing to be weeded

1/5 + fraction Summer weeded = 2/3

To solve for fraction Summer weeded, we can isolate it on one side of the equation by subtracting 1/5 from both sides:

fraction Summer weeded = 2/3 - 1/5

To subtract these fractions, we need a common denominator. The smallest common multiple of 3 and 5 is 15, so we can rewrite the fractions with 15 as the denominator:

fraction Summer weeded = 10/15 - 3/15

Now we can subtract:

fraction Summer weeded = 7/15

Therefore, Summer weeded 7/15 of the garden.

Answer 2

Explanation:

Let's start by finding the fraction of the garden that George weeded. We know that he weeded 1/5 of the garden, so the fraction that is left is:

1 - 1/5 = 4/5

Now we know that Summer weeded enough to leave 2/3 of the garden still needing to be weeded. This means that she weeded:

1 - 2/3 = 1/3

of the garden.

However, we want to find the fraction of the garden that Summer weeded relative to the total garden, not just the part that was left after George weeded. So we need to express this fraction as a fraction of the total garden.

To do this, we can use the fact that George weeded 1/5 of the garden, or equivalently, 5/5 + 1/5 = 6/5 of the garden. So the total garden is divided into 6 equal parts, each representing 1/5 of the garden.

Since George weeded 1/5 of the garden, there are 5/5 - 1/5 = 4/5 parts of the garden left. This means that 4/5 of the garden is divided into 3 equal parts, each representing 1/3 of the garden (since Summer left 2/3 of the garden to be weeded).

Therefore, the fraction of the garden that Summer weeded is:

1/3 * (4/5) = 4/15

So Summer weeded 4/15 of the garden.