Solve: $\[ \frac{5}{7} \times 4 = \\]

Feb 27, 2025 by ADMIN 39 views

$**Solve: $\frac{5}{7} \times 4$**$

Introduction

In mathematics, multiplication is a fundamental operation that involves the repeated addition of a number. When we multiply a fraction by a whole number, we need to multiply the numerator of the fraction by the whole number and keep the denominator the same. In this article, we will solve the equation $\frac{5}{7} \times 4$ and explore the concept of multiplying fractions by whole numbers.

Understanding the Problem

The given equation is $\frac{5}{7} \times 4$ . To solve this equation, we need to multiply the numerator of the fraction, which is 5, by the whole number 4. The denominator of the fraction remains the same, which is 7.

Step-by-Step Solution

To solve the equation $\frac{5}{7} \times 4$ , we will follow these steps:

Multiply the Numerator by the Whole Number

The first step is to multiply the numerator of the fraction, which is 5, by the whole number 4.

$\frac{5}{7} \times 4 = \frac{5 \times 4}{7}$

Simplify the Expression

Now, we will simplify the expression by multiplying the numerator and keeping the denominator the same.

$\frac{5 \times 4}{7} = \frac{20}{7}$

Reduce the Fraction (Optional)

If the fraction can be reduced, we will reduce it to its simplest form. In this case, the fraction $\frac{20}{7}$ cannot be reduced further.

Conclusion

In this article, we solved the equation $\frac{5}{7} \times 4$ by multiplying the numerator of the fraction by the whole number 4 and keeping the denominator the same. We also explored the concept of multiplying fractions by whole numbers and provided a step-by-step solution to the equation.

Real-World Applications

Multiplying fractions by whole numbers has many real-world applications. For example, in cooking, we may need to multiply a recipe by a certain number of people. In this case, we would multiply the ingredients by the number of people to get the correct amount. Similarly, in construction, we may need to multiply the amount of materials needed by the number of buildings to be constructed.

Common Mistakes

When multiplying fractions by whole numbers, there are several common mistakes that people make. These include:

Forgetting to multiply the numerator: When multiplying a fraction by a whole number, it is easy to forget to multiply the numerator. This can result in an incorrect answer.
Keeping the denominator the same: When multiplying a fraction by a whole number, the denominator remains the same. However, it is easy to forget this and change the denominator.
Not simplifying the expression: When multiplying a fraction by a whole number, it is essential to simplify the expression. Failing to do so can result in an incorrect answer.

Tips and Tricks

When multiplying fractions by whole numbers, there are several tips and tricks that can help. These include:

Use a multiplication chart: A multiplication chart can help you quickly multiply the numerator by the whole number.
Use a calculator: A calculator can help you quickly multiply the numerator by the whole number and simplify the expression.
Check your work: It is essential to check your work when multiplying fractions by whole numbers. This can help you catch any mistakes and ensure that you get the correct answer.

Conclusion

Q: What is the rule for multiplying fractions by whole numbers?

A: The rule for multiplying fractions by whole numbers is to multiply the numerator of the fraction by the whole number and keep the denominator the same.

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

A: To multiply a fraction by a whole number, follow these steps:

Multiply the numerator of the fraction by the whole number.
Keep the denominator the same.
Simplify the expression, if possible.

Q: What is the difference between multiplying a fraction by a whole number and multiplying two fractions?

A: The main difference between multiplying a fraction by a whole number and multiplying two fractions is that when multiplying a fraction by a whole number, the denominator remains the same, whereas when multiplying two fractions, the denominators are multiplied together.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, convert the decimal to a fraction and then multiply the fractions.

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

A: To multiply a fraction by a negative number, multiply the numerator by the negative number and keep the denominator the same. The result will be a negative fraction.

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

A: Yes, you can multiply a fraction by a mixed number. To do this, convert the mixed number to an improper fraction and then multiply the fractions.

Q: What is the order of operations when multiplying fractions by whole numbers?

A: The order of operations when multiplying fractions by whole numbers is:

Multiply the numerator of the fraction by the whole number.
Keep the denominator the same.
Simplify the expression, if possible.

Q: Can I use a calculator to multiply fractions by whole numbers?

A: Yes, you can use a calculator to multiply fractions by whole numbers. However, it is essential to check your work to ensure that the calculator is giving you the correct answer.

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

A: Some common mistakes to avoid when multiplying fractions by whole numbers include:

Forgetting to multiply the numerator.
Keeping the denominator the same.
Not simplifying the expression.
Multiplying the denominator by the whole number.

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

A: To check your work when multiplying fractions by whole numbers, follow these steps:

Multiply the numerator of the fraction by the whole number.
Keep the denominator the same.
Simplify the expression, if possible.
Check that the answer is in the correct form (i.e., a fraction or a decimal).

Q: What are some real-world applications of multiplying fractions by whole numbers?

A: Some real-world applications of multiplying fractions by whole numbers include:

Cooking: Multiplying a recipe by a certain number of people.
Construction: Multiplying the amount of materials needed by the number of buildings to be constructed.
Science: Multiplying the amount of a substance by a certain number of samples.

Conclusion

In conclusion, multiplying fractions by whole numbers is a fundamental operation in mathematics. By following the steps outlined in this article and avoiding common mistakes, you can ensure that you get the correct answer when multiplying fractions by whole numbers.