From A Two Litre Cordial, Kaupa And His Friends Drank 1.5 Litres. What Fraction Of The Cordial Did They Drink?

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Introduction

Fractions are a fundamental concept in mathematics that help us understand and represent part of a whole. In everyday life, we often encounter situations where we need to calculate fractions, such as measuring ingredients for a recipe or determining the amount of liquid left in a container. In this article, we will explore a real-life scenario where a group of friends drank a portion of a two-liter cordial, and we will calculate the fraction of the cordial they consumed.

The Problem

Kaupa and his friends drank 1.5 liters of a two-liter cordial. To determine the fraction of the cordial they drank, we need to understand the concept of fractions and how to calculate them.

What is a Fraction?

A fraction is a way to represent part of a whole. It consists of two parts: a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of equal parts we have, and the denominator represents the total number of parts the whole is divided into.

Calculating the Fraction

To calculate the fraction of the cordial Kaupa and his friends drank, we need to divide the amount they drank (1.5 liters) by the total amount of the cordial (2 liters).

Step 1: Convert the Amount to a Common Denominator

To make the calculation easier, we can convert the amount of cordial they drank (1.5 liters) to a common denominator with the total amount of the cordial (2 liters). We can do this by multiplying both numbers by 2.

1.5 liters × 2 = 3 liters 2 liters × 2 = 4 liters

Step 2: Calculate the Fraction

Now that we have a common denominator, we can calculate the fraction by dividing the amount they drank (3 liters) by the total amount of the cordial (4 liters).

3 liters ÷ 4 liters = 3/4

Interpreting the Fraction

The fraction 3/4 represents the part of the cordial that Kaupa and his friends drank. In this case, they drank 3 out of 4 parts of the cordial.

Conclusion

In conclusion, Kaupa and his friends drank 3/4 of a two-liter cordial. This example illustrates the importance of understanding fractions in real-life situations. By applying the concept of fractions, we can calculate the amount of a substance that has been consumed or remaining in a container.

Real-Life Applications

Fractions have numerous real-life applications, including:

  • Measuring ingredients for a recipe
  • Determining the amount of liquid left in a container
  • Calculating the cost of a product
  • Understanding probability and statistics

Tips and Tricks

  • When working with fractions, it's essential to have a common denominator to make calculations easier.
  • You can convert fractions to decimals by dividing the numerator by the denominator.
  • Fractions can be added, subtracted, multiplied, and divided, just like whole numbers.

Practice Problems

  1. A group of friends drank 2/3 of a 6-liter jug of juice. What fraction of the juice did they drink?
  2. A recipe calls for 3/4 cup of sugar. If you only have a 1/2 cup measuring cup, how many times will you need to fill it to get the required amount of sugar?
  3. A container holds 5/6 of a liter of water. If you add 1/4 liter of water to the container, what fraction of the container is now full?

Answer Key

  1. 4/6 or 2/3
  2. 2 times
  3. 5/6
    Fractions Q&A: Understanding and Applying Fractions in Real-Life Scenarios ====================================================================

Introduction

Fractions are a fundamental concept in mathematics that help us understand and represent part of a whole. In our previous article, we explored a real-life scenario where a group of friends drank a portion of a two-liter cordial, and we calculated the fraction of the cordial they consumed. In this article, we will answer some frequently asked questions about fractions and provide examples of how to apply them in real-life scenarios.

Q: What is a fraction?

A: A fraction is a way to represent part of a whole. It consists of two parts: a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of equal parts we have, and the denominator represents the total number of parts the whole is divided into.

Q: How do I add fractions?

A: To add fractions, we need to have a common denominator. We can convert the fractions to have a common denominator by multiplying the numerator and denominator of each fraction by the same number. For example:

1/4 + 1/4 = 2/4

We can simplify the fraction by dividing both numbers by their greatest common divisor (GCD). In this case, the GCD of 2 and 4 is 2, so we can simplify the fraction to:

1/2

Q: How do I subtract fractions?

A: To subtract fractions, we need to have a common denominator. We can convert the fractions to have a common denominator by multiplying the numerator and denominator of each fraction by the same number. For example:

3/4 - 1/4 = 2/4

We can simplify the fraction by dividing both numbers by their greatest common divisor (GCD). In this case, the GCD of 2 and 4 is 2, so we can simplify the fraction to:

1/2

Q: How do I multiply fractions?

A: To multiply fractions, we simply multiply the numerators and denominators separately. For example:

2/3 × 3/4 = 6/12

We can simplify the fraction by dividing both numbers by their greatest common divisor (GCD). In this case, the GCD of 6 and 12 is 6, so we can simplify the fraction to:

1/2

Q: How do I divide fractions?

A: To divide fractions, we can invert the second fraction (i.e., flip the numerator and denominator) and then multiply. For example:

2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way to represent part of a whole, while a decimal is a way to represent a number as a sum of powers of 10. For example:

1/2 = 0.5

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, we can divide the numerator by the denominator. For example:

1/2 = 1 ÷ 2 = 0.5

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, we can express the decimal as a sum of powers of 10 and then simplify. For example:

0.5 = 5/10 = 1/2

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example:

GCD(6, 12) = 6

Q: How do I find the GCD of two numbers?

A: We can find the GCD of two numbers by listing the factors of each number and finding the largest factor they have in common. For example:

Factors of 6: 1, 2, 3, 6 Factors of 12: 1, 2, 3, 4, 6, 12 GCD(6, 12) = 6

Conclusion

Fractions are a fundamental concept in mathematics that help us understand and represent part of a whole. By understanding how to add, subtract, multiply, and divide fractions, we can apply them in real-life scenarios. We hope this Q&A article has helped you understand and apply fractions in your everyday life.

Practice Problems

  1. Add the fractions 1/4 and 1/4.
  2. Subtract the fractions 3/4 and 1/4.
  3. Multiply the fractions 2/3 and 3/4.
  4. Divide the fractions 2/3 and 3/4.
  5. Convert the fraction 1/2 to a decimal.
  6. Convert the decimal 0.5 to a fraction.
  7. Find the GCD of 6 and 12.
  8. Add the fractions 1/2 and 1/4.

Answer Key

  1. 2/4 or 1/2
  2. 2/4 or 1/2
  3. 6/12 or 1/2
  4. 8/9
  5. 0.5
  6. 1/2
  7. 6
  8. 3/4