How to Multiply a Whole Number and a Fraction

Oct 13, 2025 by miodeya.com 127 views

**Multiply: $10 \times \frac{2}{5}$ Answer as a Whole Number**

Understanding the Problem

When we encounter a multiplication problem involving a whole number and a fraction, we need to follow a specific set of steps to arrive at the correct answer. In this case, we are given the expression $10 \times \frac{2}{5}$ , and we are asked to simplify it and express the result as a whole number.

What is Multiplication?

Multiplication is a mathematical operation that involves the repeated addition of a number. In other words, when we multiply two numbers together, we are essentially adding the first number a certain number of times, equal to the value of the second number. For example, $3 \times 4$ can be thought of as $3 + 3 + 3 + 3$ , which equals $12$ .

How to Multiply a Whole Number and a Fraction

To multiply a whole number and a fraction, we need to follow these steps:

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

Solving the Problem

Now that we understand the steps involved in multiplying a whole number and a fraction, let's apply them to the given expression $10 \times \frac{2}{5}$ .

Multiply the numerator of the fraction by the whole number: $10 \times 2 = 20$
Keep the denominator of the fraction the same: $\frac{20}{5}$
Simplify the resulting fraction: $\frac{20}{5} = 4$

Therefore, the result of multiplying $10$ and $\frac{2}{5}$ is $4$ .

Example Questions and Answers

Here are some example questions and answers to help you practice multiplying whole numbers and fractions:

Q1: $5 \times \frac{3}{4}$

A1: To solve this problem, we multiply the numerator of the fraction by the whole number: $5 \times 3 = 15$ . Then, we keep the denominator of the fraction the same: $\frac{15}{4}$ . Finally, we simplify the resulting fraction: $\frac{15}{4} = 3.75$ .

Q2: $8 \times \frac{2}{3}$

A2: To solve this problem, we multiply the numerator of the fraction by the whole number: $8 \times 2 = 16$ . Then, we keep the denominator of the fraction the same: $\frac{16}{3}$ . Finally, we simplify the resulting fraction: $\frac{16}{3} = 5.33$ .

Q3: $12 \times \frac{5}{6}$

A3: To solve this problem, we multiply the numerator of the fraction by the whole number: $12 \times 5 = 60$ . Then, we keep the denominator of the fraction the same: $\frac{60}{6}$ . Finally, we simplify the resulting fraction: $\frac{60}{6} = 10$ .

Conclusion

Multiplying a whole number and a fraction involves following a specific set of steps. We multiply the numerator of the fraction by the whole number, keep the denominator the same, and then simplify the resulting fraction, if possible. By practicing these steps, you can become more confident and proficient in multiplying whole numbers and fractions.

Frequently Asked Questions

Here are some frequently asked questions related to multiplying whole numbers and fractions:

Q1: What is the difference between multiplying a whole number and a fraction, and multiplying two fractions together?

A1: When multiplying a whole number and a fraction, we multiply the numerator of the fraction by the whole number, and keep the denominator the same. When multiplying two fractions together, we multiply the numerators together, and multiply the denominators together.

Q2: Can I simplify a fraction before multiplying it by a whole number?

A2: Yes, you can simplify a fraction before multiplying it by a whole number. However, it's often easier to multiply the fraction by the whole number first, and then simplify the resulting fraction.

Q3: What if the denominator of the fraction is not a whole number?

A3: If the denominator of the fraction is not a whole number, you can still multiply it by a whole number. However, the resulting fraction may not be a whole number. In this case, you can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.

Common Mistakes to Avoid

Here are some common mistakes to avoid when multiplying whole numbers and fractions:

Mistake 1: Forgetting to multiply the numerator by the whole number

A1: Make sure to multiply the numerator of the fraction by the whole number, and keep the denominator the same.

Mistake 2: Simplifying the fraction before multiplying it by the whole number

A2: It's often easier to multiply the fraction by the whole number first, and then simplify the resulting fraction.

Mistake 3: Not simplifying the resulting fraction

A3: Make sure to simplify the resulting fraction, if possible, to get the final answer.

Conclusion

Multiplying whole numbers and fractions involves following a specific set of steps. By practicing these steps, you can become more confident and proficient in multiplying whole numbers and fractions. Remember to multiply the numerator by the whole number, keep the denominator the same, and simplify the resulting fraction, if possible.