How many pounds of a liquid are contained in a barrel if the barrel holds 19 4/5
 ​gallons, and a gallon of the liquid weighs 9 2/3
 ​lb? answer in fraction form

To find the total weight in fraction form, we follow these steps:

1. **Convert the mixed numbers to improper fractions:**

   - The volume of the liquid in the barrel is \( 19 \frac{4}{5} \) gallons.
   - The weight of one gallon of the liquid is \( 9 \frac{2}{3} \) pounds.

   Convert these mixed numbers to improper fractions:
   \[
   19 \frac{4}{5} = \frac{19 \times 5 + 4}{5} = \frac{95 + 4}{5} = \frac{99}{5} \text{ gallons}
   \]
   \[
   9 \frac{2}{3} = \frac{9 \times 3 + 2}{3} = \frac{27 + 2}{3} = \frac{29}{3} \text{ pounds per gallon}
   \]

2. **Multiply the fractions:**
   \[
   \text{Total weight} = \frac{99}{5} \times \frac{29}{3}
   \]
   Multiply the numerators and denominators:
   \[
   \text{Total weight} = \frac{99 \times 29}{5 \times 3} = \frac{2871}{15} \text{ pounds}
   \]

So, the total weight of the liquid in the barrel is **\(\frac{2871}{15}\) pounds**.

Would you like further details or have any questions?

---

**Relative Questions:**

1. How would the fraction change if the barrel held 20 gallons instead?
2. What is the simplified form of the fraction \(\frac{2871}{15}\), if possible?
3. How can you convert this fraction into a mixed number?
4. What would the fraction be if the weight per gallon was \( 8 \frac{1}{4} \) pounds instead?
5. How would you represent the result as a decimal?

**Tip:** Keep fractions in their improper form for exact calculations before converting to mixed numbers or decimals if needed.

Learn how to calculate the weight of a liquid in a barrel given the volume in gallons and the weight per gallon. This problem involves converting mixed numbers to improper fractions and multiplying fractions to find the total weight. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation