Multiply.1. $3 \times \frac{2}{5} =$ \_\_\_\_\_3. $5 \times \frac{5}{6} =$ \_\_\_\_\_5. $8 \times \frac{3}{10} =$ \_\_\_\_\_

Understanding the Basics of Multiplication

Multiplication is a fundamental operation in mathematics that involves the repeated addition of a number. When we multiply a whole number by a fraction, we are essentially adding the fraction a certain number of times, equal to the value of the whole number. In this article, we will explore the concept of multiplying whole numbers and fractions, and provide step-by-step solutions to various problems.

Multiplying Whole Numbers and Fractions

When multiplying a whole number by a fraction, we can follow these simple steps:

1. Multiply the numerator of the fraction by the whole number.
2. Keep the denominator of the fraction the same.
3. Simplify the resulting fraction, if possible.

Let's apply these steps to the given problems:

Problem 1: $3 \times \frac{2}{5} =$

To solve this problem, we will multiply the numerator of the fraction (2) by the whole number (3), and keep the denominator the same.

Step 1: Multiply the numerator by the whole number: $2 \times 3 = 6$

Step 2: Keep the denominator the same: $\frac{6}{5}$

Step 3: Simplify the resulting fraction, if possible: $\frac{6}{5}$ cannot be simplified further.

Therefore, the solution to the problem is: $3 \times \frac{2}{5} = \frac{6}{5}$

Problem 2: $5 \times \frac{5}{6} =$

To solve this problem, we will multiply the numerator of the fraction (5) by the whole number (5), and keep the denominator the same.

Step 1: Multiply the numerator by the whole number: $5 \times 5 = 25$

Step 2: Keep the denominator the same: $\frac{25}{6}$

Step 3: Simplify the resulting fraction, if possible: $\frac{25}{6}$ cannot be simplified further.

Therefore, the solution to the problem is: $5 \times \frac{5}{6} = \frac{25}{6}$

Problem 3: $8 \times \frac{3}{10} =$

To solve this problem, we will multiply the numerator of the fraction (3) by the whole number (8), and keep the denominator the same.

Step 1: Multiply the numerator by the whole number: $3 \times 8 = 24$

Step 2: Keep the denominator the same: $\frac{24}{10}$

Step 3: Simplify the resulting fraction, if possible: $\frac{24}{10}$ can be simplified by dividing both the numerator and denominator by 2: $\frac{12}{5}$

Therefore, the solution to the problem is: $8 \times \frac{3}{10} = \frac{12}{5}$

Conclusion

Multiplying whole numbers and fractions is a fundamental operation in mathematics that involves the repeated addition of a number. By following the simple steps outlined in this article, we can solve various problems involving the multiplication of whole numbers and fractions. Remember to multiply the numerator of the fraction by the whole number, keep the denominator the same, and simplify the resulting fraction, if possible.

Practice Problems

Try solving the following problems on your own:

• $4 \times \frac{2}{3} =$
• $6 \times \frac{5}{8} =$
• $9 \times \frac{3}{4} =$

Answer Key

• $4 \times \frac{2}{3} = \frac{8}{3}$
• $6 \times \frac{5}{8} = \frac{15}{4}$
• $9 \times \frac{3}{4} = \frac{27}{4}$

Real-World Applications

Multiplying whole numbers and fractions has numerous real-world applications, including:

• Cooking: When a recipe calls for a certain amount of ingredients, we need to multiply the ingredients by the number of servings.
• Building: When building a structure, we need to multiply the length and width of the structure by the number of units.
• Finance: When calculating interest rates, we need to multiply the principal amount by the interest rate.

Conclusion

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about multiplying whole numbers and fractions.

Q: What is the difference between multiplying whole numbers and fractions?

A: Multiplying whole numbers involves repeated addition, while multiplying fractions involves multiplying the numerators and denominators separately.

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

A: To multiply a whole number by a fraction, multiply the numerator of the fraction by the whole number, and keep the denominator the same. Then, simplify the resulting fraction, if possible.

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

A: The order of operations is:

1. Multiply the numerator of the fraction by the whole number.
2. Keep the denominator the same.
3. Simplify the resulting fraction, if possible.

Q: Can I simplify a fraction before multiplying it by a whole number?

A: Yes, you can simplify a fraction before multiplying it by a whole number. However, make sure to simplify the fraction correctly to avoid errors.

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

A: To multiply a fraction by a fraction, multiply the numerators and denominators separately. Then, simplify the resulting fraction, if possible.

Q: What is the difference between multiplying fractions and multiplying whole numbers?

A: Multiplying fractions involves multiplying the numerators and denominators separately, while multiplying whole numbers involves repeated addition.

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

A: Yes, you can multiply a negative number by a fraction. When multiplying a negative number by a fraction, the result will be negative.

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

A: To multiply a decimal by a fraction, convert the decimal to a fraction, then multiply the fractions.

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

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

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

A: Multiplying whole numbers and fractions has numerous real-world applications, including:

• Cooking: When a recipe calls for a certain amount of ingredients, we need to multiply the ingredients by the number of servings.
• Building: When building a structure, we need to multiply the length and width of the structure by the number of units.
• Finance: When calculating interest rates, we need to multiply the principal amount by the interest rate.

Conclusion

In conclusion, multiplying whole numbers and fractions is a fundamental operation in mathematics that has numerous real-world applications. By understanding the basics of multiplication and following the simple steps outlined in this article, you can solve various problems involving the multiplication of whole numbers and fractions.

Practice Problems

Try solving the following problems on your own:

• $2 \times \frac{3}{4} =$
• $5 \times \frac{2}{3} =$
• $3 \times \frac{5}{6} =$

Answer Key

• $2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2}$
• $5 \times \frac{2}{3} = \frac{10}{3}$
• $3 \times \frac{5}{6} = \frac{15}{6} = \frac{5}{2}$