Calculating the Fraction of Paint Used: A Simple Mathematical Problem

Introduction

Mathematics can often be applied to real-life situations, making it both relevant and engaging. This article will explore a simple mathematical problem related to the usage of paint by Don Don. By solving this problem, we will reinforce our understanding of how to work with fractions and solve problems involving their use in everyday scenarios.

The Problem

Don Don discovered a peculiar scenario at home when he found 5/8 liters of paint. He decided to use 3/4 of this amount for his projects, such as painting some pots. The question arises: What fraction of the total paint was used?

Step-by-Step Solution

To solve this problem, we need to calculate the amount of paint Don Don used. This involves several steps:

Step 1: Calculate the Amount of Paint Used

The formula to find the amount of paint used is:

Equals frac{3}{4} times frac{5}{8} frac{3 times 5}{4 times 8} frac{15}{32}

Here, we multiplied the numerators (3 and 5) and the denominators (4 and 8) to get the resulting fraction:

Step 2: Express the Used Amount as a Fraction of the Total Paint

Next, we need to express the amount used (15/32) as a fraction of the total amount of paint (5/8). This involves dividing the used amount by the total amount:

frac{15}{32} div frac{5}{8} frac{15}{32} times frac{8}{5} frac{15 times 8}{32 times 5} frac{120}{160}

Note that we inverted the divisor fraction (5/8) and multiplied it to get the quotient.

Step 3: Simplify the Result

The result of the division is 120/160, but this fraction can be simplified. The greatest common divisor (GCD) of 120 and 160 is 40, so we divide both the numerator and the denominator by 40:

frac{120}{160} frac{120 div 40}{160 div 40} frac{3}{4}

Conclusion

To summarize, Don Don used 3/4 of the total paint he had, which is equal to 15/32 liters. This problem illustrates the practical application of fractions in everyday scenarios, reinforcing the importance of understanding mathematical concepts.

Additional Tips for Similar Problems

1. **Multiplying Fractions**: Remember to multiply the numerators together and the denominators together. This is key in finding the product of two fractions.

2. **Dividing Fractions**: To divide fractions, invert the divisor and multiply. This technique simplifies the division process.

3. **Simplification**: Always look for common factors to simplify fractions, making them easier to understand and work with.

Final Answer

Don Don used 3/4 of the total paint he had, which is equivalent to 15/32 liters. This is the fraction of paint used in this scenario.