Question

Please answer ASAP and if you do you will get Brainliest. Catherine buys a gallon of ice cream from the store. After taking it home, she eats a fifth of a gallon of ice cream. Her sister eats some of the ice cream as well. If two-thirds of the original amount of ice cream is left, then what fraction of a gallon of ice cream did her sister eat?

Answer 1

Answer:

Catherine's sister ate 2/15 gallons of the ice cream.

$\displaystyle \frac{2}{15}$.

Step-by-step explanation:

Let $x$ be the amount of ice cream that Catherine's sister ate, in gallons.

• Original amount: 1 gallon.

• What Catherine ate: $\displaystyle \frac{1}{5}$ gallons.
• What Catherine's sister ate is assumed to be $x$ gallons.

• What's left: $\displaystyle \frac{2}{3}$ gallons.

Consider the relationship:

$\text{Original amount - What Catherine ate - What Catherine's Sister ate}\\ =\text{ What's left.}$.

That is:

$\displaystyle 1- \frac{1}{5} - x = \frac{2}{3}$.

Add $x$ to both sides of this equation:

$\displaystyle 1 - \frac{1}{5} = \frac{2}{3} +x$

Substract $\displaystyle \frac{2}{3}$ from both sides:

$\displaystyle 1 - \frac{1}{5} - \frac{2}{3} = x$.

Convert the denominator of all three numbers on the left-hand side to $3 \times 5 = 15$

$\displaystyle \frac{15}{15} - \frac{3}{15} - \frac{10}{15} = x$.

$\displaystyle x = \frac{2}{15}$.

In other words, Catherine's sister ate $\displaystyle \frac{2}{15}$ gallons of the ice cream.

Answer 2

To solve this, we need to add the 1/5 of the ice cream to the 2/3 left of ice cream to find out how much her sister ate.

First, we need a common denominator. We can multiply 3 by 5 to get a common denominator easiest, since they are both multiples of it.

3*5=15

Now multiply the numerators by the amount the denominators were multiplied by.

1*3=3 so 3/15

2*5=10 so 10/15

Now, add them together.

10/15+3/15= 13/15.

Finally, subtract that amount from the original full amount of ice cream (15/15) to get the amount her sister ate, since that is the only unknown value left.

15/15-13/15=2/15.

Because 15 isn’t divisible by 2, we can’t simplify this fraction anymore.

Her sister ate 2/15 of a gallon of ice cream.

Hope this helps!