Question

Riley has

3 1/4 quarts of red paint and

4 2/3 quarts of blue paint. How many quarts of paint does Riley have in all?



7 3/12 quarts



7 3/7 quarts



7 11/12 quarts



8 3/7quarts

Answer 1

To find out how many quarts of paint Riley has in all, we need to add the amounts of red paint and blue paint together. We have:

- Red paint: \(3 \frac{1}{4}\) quarts
- Blue paint: \(4 \frac{2}{3}\) quarts

First, we convert the mixed numbers to improper fractions.

1. Convert \(3 \frac{1}{4}\) to an improper fraction:
\[
3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}
\]

2. Convert \(4 \frac{2}{3}\) to an improper fraction:
\[
4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
\]

Now we need to add \(\frac{13}{4}\) and \(\frac{14}{3}\). To do this, we need a common denominator. The least common multiple of 4 and 3 is 12.

3. Convert \(\frac{13}{4}\) to a fraction with a denominator of 12:
\[
\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}
\]

4. Convert \(\frac{14}{3}\) to a fraction with a denominator of 12:
\[
\frac{14}{3} = \frac{14 \times 4}{3 \times 4} = \frac{56}{12}
\]

Now we can add the two fractions:
\[
\frac{39}{12} + \frac{56}{12} = \frac{39 + 56}{12} = \frac{95}{12}
\]

Next, we convert \(\frac{95}{12}\) to a mixed number:
- Divide 95 by 12, which gives 7 with a remainder of 11.
Thus, \(\frac{95}{12} = 7 \frac{11}{12}\).

Therefore, the total amount of paint Riley has is:
\[
\textbf{7} \frac{11}{12} \text{ quarts}
\]

So, the answer is **7 11/12 quarts**.