Calculate The Product:$\[ 3 \frac{1}{5} \times 1 \frac{2}{3} \\]

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**Calculate the Product: A Step-by-Step Guide** =====================================================

What is the Product of Two Mixed Numbers?

In mathematics, the product of two mixed numbers is a fundamental concept that requires a clear understanding of fractions and their operations. A mixed number is a combination of a whole number and a fraction, denoted by a space or a dash between the two parts. For example, 3 1/5 and 1 2/3 are two mixed numbers.

How to Calculate the Product of Two Mixed Numbers?

To calculate the product of two mixed numbers, we need to follow a step-by-step approach. Here's a detailed guide:

Step 1: Convert the Mixed Numbers to Improper Fractions

The first step is to convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

  • To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. Then, we write the result as the new numerator over the denominator.
  • For example, to convert 3 1/5 to an improper fraction, we multiply 3 by 5 and add 1, which gives us 16/5.

Step 2: Multiply the Numerators

Once we have the improper fractions, we multiply the numerators together.

  • For example, if we have 16/5 and 8/3, we multiply 16 by 8, which gives us 128.

Step 3: Multiply the Denominators

Next, we multiply the denominators together.

  • For example, if we have 5 and 3, we multiply 5 by 3, which gives us 15.

Step 4: Write the Product as a Fraction

Now, we write the product as a fraction by dividing the product of the numerators by the product of the denominators.

  • For example, the product of 16/5 and 8/3 is 128/15.

Step 5: Simplify the Fraction (Optional)

If the fraction can be simplified, we simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD).

  • For example, the GCD of 128 and 15 is 1, so the fraction 128/15 cannot be simplified.

Example: Calculate the Product of 3 1/5 and 1 2/3

Let's calculate the product of 3 1/5 and 1 2/3 using the steps above.

  • First, we convert the mixed numbers to improper fractions:
    • 3 1/5 = 16/5
    • 1 2/3 = 5/3
  • Next, we multiply the numerators together: 16 × 5 = 80
  • Then, we multiply the denominators together: 5 × 3 = 15
  • Now, we write the product as a fraction: 80/15
  • Finally, we simplify the fraction (if possible): The GCD of 80 and 15 is 5, so we divide both the numerator and the denominator by 5 to get 16/3.

Q&A

Q: What is the product of 2 3/4 and 1 1/2?

A: To calculate the product, we first convert the mixed numbers to improper fractions: 2 3/4 = 11/4 and 1 1/2 = 3/2. Then, we multiply the numerators together: 11 × 3 = 33. Next, we multiply the denominators together: 4 × 2 = 8. Now, we write the product as a fraction: 33/8. Finally, we simplify the fraction (if possible): The GCD of 33 and 8 is 1, so the fraction 33/8 cannot be simplified.

Q: How do I calculate the product of a mixed number and a whole number?

A: To calculate the product of a mixed number and a whole number, we first convert the mixed number to an improper fraction. Then, we multiply the improper fraction by the whole number. For example, to calculate the product of 3 1/5 and 2, we first convert 3 1/5 to an improper fraction: 16/5. Then, we multiply 16/5 by 2: (16/5) × 2 = 32/5.

Q: Can I use a calculator to calculate the product of two mixed numbers?

A: Yes, you can use a calculator to calculate the product of two mixed numbers. However, it's always a good idea to understand the underlying math and perform the calculations manually to ensure accuracy and build your math skills.

Q: How do I calculate the product of two fractions with different denominators?

A: To calculate the product of two fractions with different denominators, we first find the least common multiple (LCM) of the denominators. Then, we multiply the numerators together and the denominators together, using the LCM as the new denominator. For example, to calculate the product of 1/2 and 1/3, we first find the LCM of 2 and 3, which is 6. Then, we multiply the numerators together: 1 × 1 = 1. Next, we multiply the denominators together: 2 × 3 = 6. Now, we write the product as a fraction: 1/6.

Q: Can I simplify a fraction with a negative numerator or denominator?

A: Yes, you can simplify a fraction with a negative numerator or denominator. To simplify a fraction with a negative numerator or denominator, we follow the same steps as simplifying a fraction with positive numerator and denominator. For example, to simplify the fraction -3/4, we find the GCD of 3 and 4, which is 1. Since the GCD is 1, the fraction -3/4 cannot be simplified.

Q: How do I calculate the product of a fraction and a decimal?

A: To calculate the product of a fraction and a decimal, we first convert the decimal to a fraction. Then, we multiply the fraction by the fraction. For example, to calculate the product of 1/2 and 0.5, we first convert 0.5 to a fraction: 1/2. Then, we multiply the fractions together: (1/2) × (1/2) = 1/4.

Q: Can I use a calculator to calculate the product of a fraction and a decimal?

A: Yes, you can use a calculator to calculate the product of a fraction and a decimal. However, it's always a good idea to understand the underlying math and perform the calculations manually to ensure accuracy and build your math skills.

Q: How do I calculate the product of a fraction and a percentage?

A: To calculate the product of a fraction and a percentage, we first convert the percentage to a decimal. Then, we multiply the fraction by the decimal. For example, to calculate the product of 1/2 and 25%, we first convert 25% to a decimal: 0.25. Then, we multiply the fraction by the decimal: (1/2) × 0.25 = 0.125.

Q: Can I use a calculator to calculate the product of a fraction and a percentage?

A: Yes, you can use a calculator to calculate the product of a fraction and a percentage. However, it's always a good idea to understand the underlying math and perform the calculations manually to ensure accuracy and build your math skills.

Q: How do I calculate the product of two percentages?

A: To calculate the product of two percentages, we first convert the percentages to decimals. Then, we multiply the decimals together. For example, to calculate the product of 25% and 50%, we first convert the percentages to decimals: 0.25 and 0.5. Then, we multiply the decimals together: 0.25 × 0.5 = 0.125.

Q: Can I use a calculator to calculate the product of two percentages?

A: Yes, you can use a calculator to calculate the product of two percentages. However, it's always a good idea to understand the underlying math and perform the calculations manually to ensure accuracy and build your math skills.

Q: How do I calculate the product of a fraction and a mixed number?

A: To calculate the product of a fraction and a mixed number, we first convert the mixed number to an improper fraction. Then, we multiply the fraction by the improper fraction. For example, to calculate the product of 1/2 and 3 1/4, we first convert 3 1/4 to an improper fraction: 13/4. Then, we multiply the fraction by the improper fraction: (1/2) × (13/4) = 13/8.

Q: Can I use a calculator to calculate the product of a fraction and a mixed number?

A: Yes, you can use a calculator to calculate the product of a fraction and a mixed number. However, it's always a good idea to understand the underlying math and perform the calculations manually to ensure accuracy and build your math skills.

Q: How do I calculate the product of two mixed numbers with different denominators?

A: To calculate the product of two mixed numbers with different denominators, we first convert the mixed numbers to improper fractions. Then, we multiply the numerators together and the denominators together, using the least common multiple (LCM) as the new denominator. For example, to calculate the product of