Multiply: 7 8 × 5 9 \frac{7}{8} \times \frac{5}{9} 8 7 ​ × 9 5 ​

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Introduction

Multiplication of Fractions: When we multiply two fractions, we need to multiply the numerators together and the denominators together. This is a fundamental concept in mathematics, and it's essential to understand how to multiply fractions correctly. In this article, we will explore the concept of multiplying fractions and provide a step-by-step guide on how to multiply 78×59\frac{7}{8} \times \frac{5}{9}.

Understanding Fractions

A fraction is a way of expressing a part of a whole. It consists of two parts: the numerator and the denominator. The numerator is the top number, and it represents the number of equal parts we have. The denominator is the bottom number, and it represents the total number of parts the whole is divided into. For example, in the fraction 78\frac{7}{8}, the numerator is 7, and the denominator is 8.

Multiplying Fractions

When we multiply two fractions, we need to multiply the numerators together and the denominators together. This is because the product of two fractions is equal to the product of their numerators divided by the product of their denominators. In other words, ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}.

Step-by-Step Guide to Multiplying 78×59\frac{7}{8} \times \frac{5}{9}

To multiply 78×59\frac{7}{8} \times \frac{5}{9}, we need to follow these steps:

  1. Multiply the numerators together: 7×5=357 \times 5 = 35
  2. Multiply the denominators together: 8×9=728 \times 9 = 72
  3. Write the product of the numerators as the new numerator: 3535
  4. Write the product of the denominators as the new denominator: 7272
  5. Simplify the fraction, if possible.

Simplifying the Fraction

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder. In this case, the GCD of 35 and 72 is 1, which means that the fraction 3572\frac{35}{72} is already in its simplest form.

Conclusion

Multiplying fractions is a fundamental concept in mathematics, and it's essential to understand how to multiply fractions correctly. By following the steps outlined in this article, you can multiply 78×59\frac{7}{8} \times \frac{5}{9} and simplify the fraction to its simplest form. Remember to multiply the numerators together and the denominators together, and then simplify the fraction, if possible.

Real-World Applications

Multiplying fractions has many real-world applications. For example, in cooking, you may need to multiply a recipe by a certain fraction to make a larger or smaller batch of food. In construction, you may need to multiply the dimensions of a room by a certain fraction to calculate the area or volume of the room. In finance, you may need to multiply the interest rate by a certain fraction to calculate the interest earned on an investment.

Common Mistakes to Avoid

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

  • Multiplying the numerator and denominator separately, rather than multiplying them together.
  • Forgetting to simplify the fraction, if possible.
  • Not checking the GCD of the numerator and denominator to ensure that the fraction is in its simplest form.

Tips and Tricks

Here are some tips and tricks to help you multiply fractions correctly:

  • Always multiply the numerators together and the denominators together.
  • Simplify the fraction, if possible, by finding the GCD of the numerator and denominator.
  • Check your work by multiplying the fraction by a simple fraction, such as 11\frac{1}{1}.
  • Use a calculator or a computer program to check your work, if necessary.

Final Thoughts

Multiplying fractions is a fundamental concept in mathematics, and it's essential to understand how to multiply fractions correctly. By following the steps outlined in this article, you can multiply 78×59\frac{7}{8} \times \frac{5}{9} and simplify the fraction to its simplest form. Remember to multiply the numerators together and the denominators together, and then simplify the fraction, if possible. With practice and patience, you can become proficient in multiplying fractions and apply this skill to real-world problems.

Introduction

In our previous article, we explored the concept of multiplying fractions and provided a step-by-step guide on how to multiply 78×59\frac{7}{8} \times \frac{5}{9}. In this article, we will answer some frequently asked questions about multiplying fractions and provide additional tips and tricks to help you become proficient in this skill.

Q&A

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

A: Multiplying fractions involves multiplying the numerators together and the denominators together, whereas adding fractions involves finding a common denominator and adding the numerators together.

Q: How do I know when to multiply fractions and when to add fractions?

A: You should multiply fractions when you are dealing with a problem that involves scaling or proportion, such as finding the area of a rectangle or the volume of a cube. You should add fractions when you are dealing with a problem that involves combining or comparing quantities, such as finding the total amount of money in a bank account.

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

A: Yes, you can multiply a fraction by a whole number by multiplying the numerator of the fraction by the whole number and keeping the denominator the same.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal by converting the decimal to a fraction and then multiplying the fractions together.

Q: How do I simplify a fraction after multiplying it?

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

Q: What is the greatest common divisor (GCD) and how do I find it?

A: The GCD is the largest number that divides both numbers without leaving a remainder. You can find the GCD by listing the factors of each number and finding the largest factor that they have in common.

Q: Can I use a calculator to multiply fractions?

A: Yes, you can use a calculator to multiply fractions, but you need to make sure that the calculator is set to the correct mode (e.g. fraction mode) and that you are entering the fractions correctly.

Q: How do I check my work when multiplying fractions?

A: You can check your work by multiplying the fraction by a simple fraction, such as 11\frac{1}{1}, and making sure that the result is the same as the original fraction.

Tips and Tricks

Here are some additional tips and tricks to help you become proficient in multiplying fractions:

  • Always multiply the numerators together and the denominators together.
  • Simplify the fraction, if possible, by finding the GCD of the numerator and denominator.
  • Check your work by multiplying the fraction by a simple fraction, such as 11\frac{1}{1}.
  • Use a calculator or a computer program to check your work, if necessary.
  • Practice, practice, practice! The more you practice multiplying fractions, the more comfortable you will become with the process.

Common Mistakes to Avoid

Here are some common mistakes to avoid when multiplying fractions:

  • Multiplying the numerator and denominator separately, rather than multiplying them together.
  • Forgetting to simplify the fraction, if possible.
  • Not checking the GCD of the numerator and denominator to ensure that the fraction is in its simplest form.
  • Not using a calculator or a computer program to check your work, if necessary.

Final Thoughts

Multiplying fractions is a fundamental concept in mathematics, and it's essential to understand how to multiply fractions correctly. By following the steps outlined in this article and practicing regularly, you can become proficient in multiplying fractions and apply this skill to real-world problems. Remember to always multiply the numerators together and the denominators together, and then simplify the fraction, if possible. With practice and patience, you can become a master of multiplying fractions!