Question

Ellen mix is 1/3 cup of orange juice with 5/6 cups of lemonade to make fruit punch. Then she adds 1 2/3 cups of soda. Use the properties of addition to find how many cups of fruit punch she makes show your work

Answer 1

Ellen makes 17/6 cups of fruit punch when combining 1/3 cup of orange juice, 5/6 cups of lemonade, and 1 2/3 cups of soda.

Step-by-step explanation:

To find out how many cups of fruit punch Ellen makes, we need to add together the amounts of each ingredient she uses. She mixes 1/3 cup of orange juice, 5/6 cups of lemonade, and 1 2/3 cups of soda. These fractions need to be added together to get the total amount of fruit punch.

Let's add the fractions step by step:

1. Start with the fraction of orange juice and lemonade: 1/3 cup + 5/6 cup.
2. To add these, we need a common denominator. The smallest common denominator for 3 and 6 is 6.
3. So, converting 1/3 cup to a fraction with a denominator of 6 gives us 2/6. Now we add 2/6 cup + 5/6 cup = 7/6 cups.
4. Next, we add the soda: 7/6 cups + 1 2/3 cups.
5. First, we express 1 2/3 cups as an improper fraction, which is 5/3 cups.
6. We now need a common denominator for 6 and 3, which is 6.
7. So we convert 5/3 to a fraction with a denominator of 6, which is 10/6 cups.
8. Finally, we add the two fractions: 7/6 cups + 10/6 cups = 17/6 cups.

Ellen makes 17/6 cups of fruit punch, when all the ingredients are combined.

Answer 2

2 5/6 cups

STEP-BY-STEP EXPLANATION:

To find the total cups, we must add the number of cups in each case, like this:

`(1)/(3)+(5)/(6)+1(2)/(3)`

For ease, we'll convert each fraction so that they all have the same denominator:

`\begin{gathered} (1)/(3)=(2)/(6) \\ (5)/(6) \\ 1(2)/(3)=(5)/(3)=(10)/(6) \\ \text{therefore:} \\ (2)/(6)+(5)/(6)+(10)/(6)=(2+5+10)/(6)=(17)/(6) \\ (17)/(6)=2(5)/(6) \end{gathered}`

That is to say that in total there are 2 5/6 cups of fruit punch