Ana And Luis Are Cooking Together, Ana USA 3/4 Of One Kilo Of Sugar And Luis USA 2/3 Of A Kilo Of Sugar. What Fraction Have You Used In Total?

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Introduction

Ana and Luis are cooking together, and they both need to use sugar for their recipe. Ana uses 3/4 of one kilo of sugar, while Luis uses 2/3 of a kilo of sugar. The question is, what fraction of sugar have they used in total? In this article, we will explore how to add fractions with different denominators and find the total amount of sugar used.

Understanding the Problem

To solve this problem, we need to understand the concept of adding fractions with different denominators. When we add fractions, we need to find a common denominator, which is the least common multiple (LCM) of the two denominators. In this case, the denominators are 4 and 3.

Finding the Least Common Multiple (LCM)

The LCM of 4 and 3 is 12. To find the LCM, we can list the multiples of each number and find the smallest multiple that is common to both.

  • Multiples of 4: 4, 8, 12, 16, 20, ...
  • Multiples of 3: 3, 6, 9, 12, 15, ...

As we can see, the smallest multiple that is common to both is 12. Therefore, the LCM of 4 and 3 is 12.

Converting Fractions to Have a Common Denominator

Now that we have found the LCM, we can convert both fractions to have a denominator of 12.

  • Ana's fraction: 3/4 = (3 x 3) / (4 x 3) = 9/12
  • Luis's fraction: 2/3 = (2 x 4) / (3 x 4) = 8/12

Adding the Fractions

Now that both fractions have a common denominator, we can add them together.

9/12 + 8/12 = 17/12

Simplifying the Fraction

The fraction 17/12 is already in its simplest form, so we don't need to simplify it further.

Conclusion

Ana and Luis have used a total of 17/12 of a kilo of sugar. This means that they have used 17 parts out of 12 equal parts of a kilo of sugar.

Real-World Applications

This problem may seem simple, but it has real-world applications in cooking, science, and engineering. When we are working with fractions, we need to be able to add and subtract them in order to solve problems. This skill is essential in many fields, and it is a fundamental concept in mathematics.

Tips and Tricks

Here are a few tips and tricks to help you add fractions with different denominators:

  • Always find the LCM of the two denominators.
  • Convert both fractions to have a common denominator.
  • Add the numerators (the numbers on top) and keep the denominator the same.
  • Simplify the fraction, if possible.

Practice Problems

Here are a few practice problems to help you practice adding fractions with different denominators:

  • 1/2 + 1/3 = ?
  • 2/5 + 3/4 = ?
  • 3/8 + 1/6 = ?

Answer Key

Here are the answers to the practice problems:

  • 1/2 + 1/3 = 5/6
  • 2/5 + 3/4 = 31/20
  • 3/8 + 1/6 = 13/24

Conclusion

Adding fractions with different denominators may seem like a daunting task, but it is a fundamental concept in mathematics. By following the steps outlined in this article, you can add fractions with different denominators and solve problems in cooking, science, and engineering. Remember to always find the LCM, convert both fractions to have a common denominator, add the numerators, and simplify the fraction, if possible. With practice and patience, you will become a master of adding fractions with different denominators.