15 1/5+12 2/5+? =53 1/15

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Introduction

Mathematics is a fascinating subject that involves solving equations, inequalities, and other mathematical problems. In this article, we will explore a math puzzle that involves adding fractions and mixed numbers. The puzzle is as follows: 15 1/5 + 12 2/5 + ? = 53 1/15. Our goal is to find the missing value that makes the equation true.

Understanding Mixed Numbers

Before we dive into solving the puzzle, let's understand what mixed numbers are. A mixed number is a combination of a whole number and a fraction. For example, 15 1/5 is a mixed number that consists of a whole number 15 and a fraction 1/5. To add mixed numbers, we need to add the whole numbers and the fractions separately.

Adding Fractions and Mixed Numbers

To add fractions and mixed numbers, we need to follow these steps:

  1. Add the whole numbers.
  2. Add the fractions.
  3. Combine the results.

Let's apply these steps to the given puzzle: 15 1/5 + 12 2/5 + ? = 53 1/15.

Step 1: Add the Whole Numbers

The whole numbers in the puzzle are 15 and 12. Let's add them:

15 + 12 = 27

Step 2: Add the Fractions

The fractions in the puzzle are 1/5 and 2/5. To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 5 and 5 is 5. Therefore, we can add the fractions as follows:

1/5 + 2/5 = 3/5

Step 3: Combine the Results

Now that we have added the whole numbers and the fractions, let's combine the results:

27 + 3/5

To combine the whole number and the fraction, we need to convert the whole number to a fraction with the same denominator. The least common multiple (LCM) of 1 and 5 is 5. Therefore, we can convert the whole number 27 to a fraction as follows:

27 = 135/5

Now that we have the whole number as a fraction, let's combine the results:

135/5 + 3/5

Step 4: Add the Fractions

Now that we have the whole number and the fraction with the same denominator, let's add the fractions:

135/5 + 3/5 = 138/5

Step 5: Simplify the Fraction

The fraction 138/5 can be simplified by dividing the numerator and the denominator by their greatest common divisor (GCD). The GCD of 138 and 5 is 1. Therefore, the fraction 138/5 cannot be simplified further.

Step 6: Convert the Fraction to a Mixed Number

To convert the fraction 138/5 to a mixed number, we need to divide the numerator by the denominator:

138 ÷ 5 = 27 with a remainder of 3

Therefore, the mixed number is 27 3/5.

Step 7: Find the Missing Value

Now that we have the result of the addition, let's find the missing value that makes the equation true:

15 1/5 + 12 2/5 + ? = 53 1/15

We know that the result of the addition is 27 3/5. Therefore, the missing value must be:

53 1/15 - 27 3/5

Step 8: Subtract the Mixed Numbers

To subtract the mixed numbers, we need to subtract the whole numbers and the fractions separately.

Step 8.1: Subtract the Whole Numbers

The whole numbers in the puzzle are 53 and 27. Let's subtract them:

53 - 27 = 26

Step 8.2: Subtract the Fractions

The fractions in the puzzle are 1/15 and 3/5. To subtract these fractions, we need to find a common denominator. The least common multiple (LCM) of 15 and 5 is 15. Therefore, we can subtract the fractions as follows:

1/15 - 3/5 = 1/15 - 9/15 = -8/15

Step 8.3: Combine the Results

Now that we have subtracted the whole numbers and the fractions, let's combine the results:

26 - 8/15

To combine the whole number and the fraction, we need to convert the whole number to a fraction with the same denominator. The least common multiple (LCM) of 1 and 15 is 15. Therefore, we can convert the whole number 26 to a fraction as follows:

26 = 390/15

Now that we have the whole number as a fraction, let's combine the results:

390/15 - 8/15

Step 8.4: Subtract the Fractions

Now that we have the whole number and the fraction with the same denominator, let's subtract the fractions:

390/15 - 8/15 = 382/15

Step 8.5: Simplify the Fraction

The fraction 382/15 can be simplified by dividing the numerator and the denominator by their greatest common divisor (GCD). The GCD of 382 and 15 is 1. Therefore, the fraction 382/15 cannot be simplified further.

Step 8.6: Convert the Fraction to a Mixed Number

To convert the fraction 382/15 to a mixed number, we need to divide the numerator by the denominator:

382 ÷ 15 = 25 with a remainder of 7

Therefore, the mixed number is 25 7/15.

The final answer is: 25 7/15

Introduction

In our previous article, we explored a math puzzle that involved adding fractions and mixed numbers. The puzzle was as follows: 15 1/5 + 12 2/5 + ? = 53 1/15. We found the missing value that makes the equation true to be 25 7/15. In this article, we will answer some frequently asked questions related to the puzzle.

Q&A

Q: What is the difference between a fraction and a mixed number?

A: A fraction is a number that represents a part of a whole, while a mixed number is a combination of a whole number and a fraction. For example, 1/2 is a fraction, while 2 1/2 is a mixed number.

Q: How do you add fractions and mixed numbers?

A: To add fractions and mixed numbers, you need to add the whole numbers and the fractions separately. For example, to add 2 1/2 and 3 1/4, you would add the whole numbers (2 + 3 = 5) and the fractions (1/2 + 1/4 = 3/4).

Q: What is the least common multiple (LCM) of two numbers?

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. For example, the LCM of 4 and 6 is 12.

Q: How do you convert a fraction to a mixed number?

A: To convert a fraction to a mixed number, you need to divide the numerator by the denominator. For example, to convert 7/4 to a mixed number, you would divide 7 by 4, which gives you 1 with a remainder of 3. Therefore, 7/4 is equal to 1 3/4.

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

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6.

Q: How do you subtract fractions and mixed numbers?

A: To subtract fractions and mixed numbers, you need to subtract the whole numbers and the fractions separately. For example, to subtract 2 1/2 from 3 1/4, you would subtract the whole numbers (3 - 2 = 1) and the fractions (1/4 - 1/2 = -1/4).

Q: What is the difference between a numerator and a denominator?

A: A numerator is the top number in a fraction, while a denominator is the bottom number in a fraction. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.

Q: How do you simplify a fraction?

A: To simplify a fraction, you need to divide the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify 6/8, you would divide both numbers by 2, which gives you 3/4.

Conclusion

In this article, we answered some frequently asked questions related to the math puzzle 15 1/5 + 12 2/5 + ? = 53 1/15. We hope that this article has provided you with a better understanding of fractions and mixed numbers, and how to add and subtract them.

Additional Resources

  • Math is Fun: A website that provides math lessons and exercises for students of all ages.
  • Khan Academy: A website that provides free online math lessons and exercises.
  • Mathway: A website that provides math problem-solving tools and resources.

The final answer is: 25 7/15