Multiply. Write Your Answer As A Fraction In Simplest Form. 4 7 × 1 5 × 7 9 \frac{4}{7} \times \frac{1}{5} \times \frac{7}{9} 7 4 ​ × 5 1 ​ × 9 7 ​

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Introduction

Multiplication of fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together. In this article, we will explore the process of multiplying fractions, including the rules and steps involved. We will also provide a step-by-step solution to the problem 47×15×79\frac{4}{7} \times \frac{1}{5} \times \frac{7}{9}.

What is a Fraction?

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, the fraction 12\frac{1}{2} represents one half of a whole.

Rules of Multiplying Fractions

When multiplying fractions, there are several rules to follow:

  • Rule 1: Multiply the numerators together to get the new numerator.
  • Rule 2: Multiply the denominators together to get the new denominator.
  • Rule 3: Simplify the resulting fraction, if possible.

Step-by-Step Solution to the Problem

Now, let's apply these rules to the problem 47×15×79\frac{4}{7} \times \frac{1}{5} \times \frac{7}{9}.

Step 1: Multiply the Numerators

To multiply the numerators, we simply multiply the numbers together:

4 × 1 × 7 = 28

Step 2: Multiply the Denominators

To multiply the denominators, we simply multiply the numbers together:

7 × 5 × 9 = 315

Step 3: Write the Resulting Fraction

Now, we can write the resulting fraction by combining the new numerator and denominator:

28315\frac{28}{315}

Step 4: Simplify the Fraction (if possible)

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 28 and 315 is 7. We can divide both the numerator and denominator by 7 to simplify the fraction:

28÷7315÷7=445\frac{28 ÷ 7}{315 ÷ 7} = \frac{4}{45}

Conclusion

In conclusion, multiplying fractions involves following a set of rules and steps. By multiplying the numerators and denominators together, and then simplifying the resulting fraction, we can find the product of two or more fractions. In this article, we applied these rules to the problem 47×15×79\frac{4}{7} \times \frac{1}{5} \times \frac{7}{9} and found the resulting fraction to be 445\frac{4}{45}.

Common Mistakes to Avoid

When multiplying fractions, there are several common mistakes to avoid:

  • Mistake 1: Forgetting to multiply the denominators together.
  • Mistake 2: Not simplifying the resulting fraction, if possible.
  • Mistake 3: Not following the order of operations (PEMDAS).

Real-World Applications

Multiplication of fractions has several real-world applications, including:

  • 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 rules of multiplying fractions to find the correct amount.
  • Science: In scientific experiments, you may need to multiply fractions to find the concentration of a solution or the amount of a substance.
  • Finance: When investing in stocks or bonds, you may need to multiply fractions to find the return on investment.

Practice Problems

To practice multiplying fractions, try the following problems:

  • 23×34×45\frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}
  • 56×23×34\frac{5}{6} \times \frac{2}{3} \times \frac{3}{4}
  • 34×45×56\frac{3}{4} \times \frac{4}{5} \times \frac{5}{6}

Conclusion

Introduction

In our previous article, we explored the concept of multiplying fractions and provided a step-by-step guide to solving the problem 47×15×79\frac{4}{7} \times \frac{1}{5} \times \frac{7}{9}. In this article, we will answer some frequently asked questions about multiplying fractions.

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, you need to find the greatest common divisor (GCD) of the numerator and denominator. You can then divide both the numerator and denominator by the GCD to simplify the fraction.

Q: What is the difference between multiplying fractions and adding fractions?

A: Multiplying fractions involves multiplying the numerators and denominators together, while adding fractions involves adding the numerators together and keeping the same denominator.

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

A: Yes, you can multiply a fraction by a whole number. To do this, you simply multiply the numerator by the whole number and keep the same denominator.

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.

Q: What is the order of operations for multiplying fractions?

A: The order of operations for multiplying fractions is:

  1. Multiply the numerators together.
  2. Multiply the denominators together.
  3. Simplify the resulting fraction, if possible.

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

A: Yes, you can multiply a negative fraction by a positive fraction. The result will be a negative fraction.

Q: How do I multiply a fraction by a fraction with a variable?

A: To multiply a fraction by a fraction with a variable, you can multiply the numerators together and multiply the denominators together. You can then simplify the resulting fraction, if possible.

Q: What are some common mistakes to avoid when multiplying fractions?

A: Some common mistakes to avoid when multiplying fractions include:

  • Forgetting to multiply the denominators together.
  • Not simplifying the resulting fraction, if possible.
  • Not following the order of operations (PEMDAS).

Q: How do I apply the rules of multiplying fractions to real-world problems?

A: You can apply the rules of multiplying fractions to real-world problems by using the concept of multiplication to solve problems involving fractions. For example, you can use the rules of multiplying fractions to find the area of a rectangle or the volume of a cube.

Conclusion

In conclusion, multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together. By following the rules and steps outlined in this article, you can multiply fractions with ease. Remember to multiply the numerators and denominators together, and then simplify the resulting fraction, if possible. With practice, you will become proficient in multiplying fractions and be able to apply this skill to real-world problems.

Practice Problems

To practice multiplying fractions, try the following problems:

  • 23×34×45\frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}
  • 56×23×34\frac{5}{6} \times \frac{2}{3} \times \frac{3}{4}
  • 34×45×56\frac{3}{4} \times \frac{4}{5} \times \frac{5}{6}

Real-World Applications

Multiplication of fractions has several real-world applications, including:

  • 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 rules of multiplying fractions to find the correct amount.
  • Science: In scientific experiments, you may need to multiply fractions to find the concentration of a solution or the amount of a substance.
  • Finance: When investing in stocks or bonds, you may need to multiply fractions to find the return on investment.

Conclusion

In conclusion, multiplication of fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together. By following the rules and steps outlined in this article, you can multiply fractions with ease. Remember to multiply the numerators and denominators together, and then simplify the resulting fraction, if possible. With practice, you will become proficient in multiplying fractions and be able to apply this skill to real-world problems.