6 × 2 6 = 6 \times \frac{2}{6} = 6 × 6 2 ​ =

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Understanding the Problem

When dealing with multiplication of fractions, it's essential to understand the concept of multiplying numerators and denominators separately. In this problem, we are given the expression 6×266 \times \frac{2}{6}, and we need to find the product.

Breaking Down the Problem

To solve this problem, we can follow the order of operations (PEMDAS):

  1. Multiply the numerator (6) with the numerator of the fraction (2).
  2. Multiply the denominator (6) with the denominator of the fraction (6).

Step-by-Step Solution

Step 1: Multiply the Numerators

The numerator of the expression is 6, and the numerator of the fraction is 2. To multiply these two numbers, we simply multiply them together:

6 × 2 = 12

Step 2: Multiply the Denominators

The denominator of the expression is 6, and the denominator of the fraction is also 6. To multiply these two numbers, we simply multiply them together:

6 × 6 = 36

Simplifying the Expression

Now that we have multiplied the numerators and denominators, we can simplify the expression by dividing the numerator by the denominator:

12 ÷ 36 = 1/3

Conclusion

In conclusion, the product of 6×266 \times \frac{2}{6} is 13\frac{1}{3}. This is because when we multiply the numerators and denominators separately, we get 12 and 36, respectively. Dividing the numerator by the denominator gives us the final result of 13\frac{1}{3}.

Real-World Applications

Multiplication of fractions has many real-world applications, such as:

  • Cooking: When a recipe calls for a certain amount of an ingredient, and you need to multiply it by a fraction, you can use the concept of multiplying fractions to get the correct amount.
  • Science: In scientific experiments, you may need to multiply measurements by fractions to get the correct results.
  • Finance: When calculating interest rates or investment returns, you may need to multiply fractions to get the correct amount.

Common Mistakes to Avoid

When multiplying fractions, it's essential to avoid common mistakes such as:

  • Forgetting to multiply the denominators: Make sure to multiply the denominators separately to get the correct result.
  • Not simplifying the expression: Simplify the expression by dividing the numerator by the denominator to get the final result.

Tips and Tricks

Here are some tips and tricks to help you solve multiplication of fractions:

  • Use a calculator: If you're struggling to multiply fractions by hand, use a calculator to get the correct result.
  • Break down the problem: Break down the problem into smaller steps to make it easier to solve.
  • Check your work: Double-check your work to ensure that you've multiplied the numerators and denominators correctly.

Conclusion

In conclusion, multiplication of fractions is a fundamental concept in mathematics that has many real-world applications. By following the order of operations and avoiding common mistakes, you can solve multiplication of fractions with ease. Remember to break down the problem into smaller steps, use a calculator if needed, and check your work to ensure that you've got the correct result.

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Frequently Asked Questions

Q: What is the product of 4×384 \times \frac{3}{8}?

A: To find the product, we multiply the numerators (4 and 3) and denominators (1 and 8) separately:

4 × 3 = 12 1 × 8 = 8

Then, we simplify the expression by dividing the numerator by the denominator:

12 ÷ 8 = 1.5

Q: How do I multiply a fraction by a whole number?

A: To multiply a fraction by a whole number, you can multiply the numerator of the fraction by the whole number, and keep the denominator the same. For example:

3 × 25\frac{2}{5} = 3×25\frac{3 \times 2}{5} = 65\frac{6}{5}

Q: What is the product of 2×562 \times \frac{5}{6}?

A: To find the product, we multiply the numerators (2 and 5) and denominators (1 and 6) separately:

2 × 5 = 10 1 × 6 = 6

Then, we simplify the expression by dividing the numerator by the denominator:

10 ÷ 6 = 1.67

Q: Can I multiply a fraction by a fraction with a different denominator?

A: Yes, you can multiply a fraction by a fraction with a different denominator. To do this, you need to find the least common multiple (LCM) of the two denominators, and then multiply the numerators and denominators separately. For example:

23×45\frac{2}{3} \times \frac{4}{5} = 2×43×5\frac{2 \times 4}{3 \times 5} = 815\frac{8}{15}

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, you can divide the numerator by the denominator. For example:

128\frac{12}{8} = 1.5

Q: Can I multiply a negative number by a fraction?

A: Yes, you can multiply a negative number by a fraction. To do this, you need to multiply the numerator and denominator separately, and then apply the negative sign to the result. For example:

−3×25-3 \times \frac{2}{5} = −3×25\frac{-3 \times 2}{5} = −65\frac{-6}{5}

Q: How do I multiply a fraction by a decimal?

A: To multiply a fraction by a decimal, you can convert the decimal to a fraction, and then multiply the fractions together. For example:

23×0.5\frac{2}{3} \times 0.5 = 23×12\frac{2}{3} \times \frac{1}{2} = 2×13×2\frac{2 \times 1}{3 \times 2} = 26\frac{2}{6} = 13\frac{1}{3}

Conclusion

In conclusion, multiplication of fractions is a fundamental concept in mathematics that has many real-world applications. By following the order of operations and avoiding common mistakes, you can solve multiplication of fractions with ease. Remember to break down the problem into smaller steps, use a calculator if needed, and check your work to ensure that you've got the correct result.