Calculating the Total Mass of Packed Beans

Oct 13, 2025 by talynt.org 51 views

Introduction

In this intriguing mathematical puzzle, we are presented with a scenario where Mdm Tan has 3 kg of beans and packs some of them into 8 packets. Each packet contains a specific mass of beans, and we are tasked with determining the mass of the beans that were not packed. This problem requires us to apply our understanding of fractions and algebraic thinking to unravel the mystery of Mdm Tan's beans.

The Problem

Mdm Tan has 3 kg of beans, which she packs into 8 packets. Each packet of beans has a mass of $$\frac{1}{5} \text{ kg}$$. To find the mass of the beans that were not packed, we need to first calculate the total mass of the beans packed in the 8 packets.

Calculating the Total Mass of Packed Beans

Since each packet contains $$\frac{1}{5} \text{ kg}$$ of beans, the total mass of the beans packed in the 8 packets can be calculated as follows:

\text{Total mass of packed beans} = 8 \times \frac{1}{5} \text{ kg}

\text{Total mass of packed beans} = \frac{8}{5} \text{ kg}

Understanding the Fraction

The fraction $$\frac{8}{5}$$ represents the total mass of the beans packed in the 8 packets. To better understand this fraction, let's break it down into its constituent parts:

The numerator, 8, represents the number of packets.
The denominator, 5, represents the mass of each packet in kilograms.

Finding the Mass of Unpacked Beans

Now that we have calculated the total mass of the packed beans, we can find the mass of the unpacked beans by subtracting the total mass of the packed beans from the total mass of the beans:

\text{Mass of unpacked beans} = \text{Total mass of beans} - \text{Total mass of packed beans}

\text{Mass of unpacked beans} = 3 \text{ kg} - \frac{8}{5} \text{ kg}

To perform this subtraction, we need to find a common denominator for the two terms. Since the denominator of the fraction is 5, we can multiply the whole number 3 by 5/5 to make the denominators the same:

\text{Mass of unpacked beans} = \frac{15}{5} \text{ kg} - \frac{8}{5} \text{ kg}

Now we can subtract the two fractions:

\text{Mass of unpacked beans} = \frac{15}{5} \text{ kg} - \frac{8}{5} \text{ kg}

\text{Mass of unpacked beans} = \frac{15 - 8}{5} \text{ kg}

\text{Mass of unpacked beans} = \frac{7}{5} \text{ kg}

Conclusion

In this mathematical puzzle, we have successfully unraveled the mystery of Mdm Tan's beans. By applying our understanding of fractions and algebraic thinking, we have calculated the mass of the beans that were not packed. The mass of the unpacked beans is $$\frac{7}{5} \text{ kg}$$, which is equivalent to 1.4 kg.

Real-World Applications

This problem may seem like a simple mathematical exercise, but it has real-world applications in various fields such as:

Cooking: When measuring ingredients for a recipe, it's essential to understand fractions and decimals to ensure accurate measurements.
Science: In scientific experiments, precise measurements are crucial to obtain accurate results.
Engineering: Engineers use mathematical calculations to design and build structures, machines, and systems.

Tips and Tricks

When working with fractions, it's essential to understand the concept of equivalent ratios.
To add or subtract fractions, find a common denominator and then perform the operation.
When multiplying or dividing fractions, multiply or divide the numerators and denominators separately.

Practice Problems

A bookshelf has 12 shelves, and each shelf can hold 3 books. If the bookshelf is currently empty, how many books can be placed on it in total?
A bakery sells 240 loaves of bread per day. If each loaf weighs 0.25 kg, how many kilograms of bread are sold per day?
A car travels 250 miles in 5 hours. If the car travels at a constant speed, how many miles does it travel per hour?

Solutions

The bookshelf can hold a total of 12 x 3 = 36 books.
The bakery sells 240 x 0.25 = 60 kg of bread per day.
The car travels 250 / 5 = 50 miles per hour.

Conclusion

Introduction

In our previous article, we explored the mathematical puzzle of Mdm Tan's beans, where she packed some of her 3 kg of beans into 8 packets, each containing $$\frac{1}{5} \text{ kg}$$ of beans. We calculated the mass of the beans that were not packed and discovered that it was $$\frac{7}{5} \text{ kg}$$, equivalent to 1.4 kg. In this article, we will answer some frequently asked questions about this puzzle and provide additional insights.

Q&A

Q: What is the total mass of the packed beans?

A: The total mass of the packed beans is $$\frac{8}{5} \text{ kg}$$.

Q: How did you calculate the total mass of the packed beans?

A: We calculated the total mass of the packed beans by multiplying the number of packets (8) by the mass of each packet ($$\frac{1}{5} \text{ kg}$$).

Q: What is the mass of the unpacked beans?

A: The mass of the unpacked beans is $$\frac{7}{5} \text{ kg}$$, equivalent to 1.4 kg.

Q: How did you calculate the mass of the unpacked beans?

A: We calculated the mass of the unpacked beans by subtracting the total mass of the packed beans from the total mass of the beans (3 kg).

Q: What is the significance of the fraction $$\frac{7}{5}$$?

A: The fraction $$\frac{7}{5}$$ represents the mass of the unpacked beans, which is equivalent to 1.4 kg.

Q: Can you explain the concept of equivalent ratios?

A: Yes, equivalent ratios are ratios that have the same value, but are expressed in different forms. For example, the ratio 2:3 is equivalent to the ratio 4:6, because both ratios have the same value.

Q: How do you add or subtract fractions?

A: To add or subtract fractions, you need to find a common denominator and then perform the operation. For example, to add $$\frac1}{2}$$ and $$\frac{1}{4}$$, you need to find a common denominator, which is 4. Then, you can add the fractions $$\frac{2{4} + \frac{1}{4} = \frac{3}{4}$$.

Q: Can you explain the concept of multiplying or dividing fractions?

A: Yes, when multiplying or dividing fractions, you multiply or divide the numerators and denominators separately. For example, to multiply $$\frac1}{2}$$ and $$\frac{3}{4}$$, you multiply the numerators (1 and 3) and the denominators (2 and 4) separately $$\frac{1 \times 3{2 \times 4} = \frac{3}{8}$$.

Additional Insights

The concept of equivalent ratios is essential in mathematics, as it allows us to compare and manipulate ratios in different forms.
When working with fractions, it's essential to find a common denominator to perform addition or subtraction.
Multiplying or dividing fractions involves multiplying or dividing the numerators and denominators separately.

Practice Problems

A bookshelf has 12 shelves, and each shelf can hold 3 books. If the bookshelf is currently empty, how many books can be placed on it in total?
A bakery sells 240 loaves of bread per day. If each loaf weighs 0.25 kg, how many kilograms of bread are sold per day?
A car travels 250 miles in 5 hours. If the car travels at a constant speed, how many miles does it travel per hour?

Solutions

The bookshelf can hold a total of 12 x 3 = 36 books.
The bakery sells 240 x 0.25 = 60 kg of bread per day.
The car travels 250 / 5 = 50 miles per hour.

Conclusion

In conclusion, this Q&A article has provided additional insights and explanations for the mathematical puzzle of Mdm Tan's beans. We have answered frequently asked questions and provided practice problems to help readers reinforce their understanding of mathematical concepts.