Understanding the multiplication of fractions, especially when they are mixed numbers, can be crucial for various applications in mathematics and daily life. One common problem is determining the value of 3 1/2 × 2/3. This article will delve into the step-by-step method to solve this problem and explore different methods and applications of such calculations.

Converting 3 1/2 to an Improper Fraction

The process of multiplying 3 1/2 by 2/3 starts with converting the mixed number 3 1/2 into an improper fraction. A mixed number is composed of a whole number and a proper fraction. To convert 3 1/2 into an improper fraction:

Multiply the whole number (3) by the denominator of the fraction (2). Add the numerator of the fraction (1) to the result from step one. The sum becomes the new numerator, and the denominator remains unchanged.

Following these steps for 3 1/2:

3 × 2 6 6 1 7 The improper fraction is

Multiplying the Improper Fraction by a Proper Fraction

Once the mixed number has been converted to an improper fraction, the next step is to multiply it by the proper fraction 2/3:

When multiplying fractions, multiply the numerators together and the denominators together:

Simplifying this expression:

The fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

The fraction can be converted back to a mixed number:

Alternative Methods of Calculation

The problem can also be solved using other methods, as shown below:

3 × 2/3 6/3 2 (Without the need for conversion) 3 × 2/3 3 × (2 ÷ 3) 3 × 0.6666666666666667 2 (Decimal equivalent)

Practical Applications

Fraction multiplication is fundamental in many practical applications. For instance, in culinary arts, it is common to divide or multiply ingredients based on the number of servings. If a recipe calls for 3 1/2 cups of flour and you only need 2/3 of the recipe, the calculation would be 3 1/2 × 2/3 to determine the exact amount of flour required.

Conclusion

Understanding how to multiply by is a valuable skill in mathematics. The method involves converting the mixed number into an improper fraction, multiplying the fractions, and simplifying the result. Whether calculating in a culinary context or solving a simple arithmetic problem, the principles remain the same. Practice these techniques to enhance your proficiency in handling fractions.