Question

solve the following problems. draw a picture, and write the number sentence that proves the answer. simplify your answer, if possible. 2. sam made \\(\frac{2}{3}\\) liter of punch and \\(\frac{3}{4}\\) liter of tea to take to a party. how many liters of beverages did sa bring to the party?

Explanation:

Step1: Identify the operation

To find the total liters of beverages, we need to add the liters of punch and tea. So the operation is addition: $\frac{2}{3} + \frac{3}{4}$.

Step2: Find a common denominator

The least common denominator of 3 and 4 is 12. Convert the fractions: $\frac{2}{3} = \frac{2\times4}{3\times4} = \frac{8}{12}$ and $\frac{3}{4} = \frac{3\times3}{4\times3} = \frac{9}{12}$.

Step3: Add the fractions

Now add the two fractions with the common denominator: $\frac{8}{12} + \frac{9}{12} = \frac{8 + 9}{12} = \frac{17}{12}$.

Step4: Simplify (if possible)

$\frac{17}{12}$ can be written as a mixed number: $1\frac{5}{12}$.

(For the picture, you can draw two rectangles, one divided into 3 equal parts with 2 parts shaded to represent $\frac{2}{3}$, and another divided into 4 equal parts with 3 parts shaded to represent $\frac{3}{4}$. Then, to add them, convert both to twelfths: the first rectangle would have 8 out of 12 parts shaded, the second 9 out of 12, and combined they have 17 out of 12 parts shaded, which is $1\frac{5}{12}$.)

Answer:

The total liters of beverages Sam brought to the party is $\boldsymbol{1\frac{5}{12}}$ liters (or $\frac{17}{12}$ liters). The number sentence is $\frac{2}{3} + \frac{3}{4} = \frac{8}{12} + \frac{9}{12} = \frac{17}{12} = 1\frac{5}{12}$.