Multiply.$\frac{4}{5} \times 20$

Mar 1, 2025 by ADMIN 33 views

$Multiply.$\frac{4}{5} \times 20$$

Introduction

When it comes to multiplying fractions and whole numbers, it's essential to understand the rules and procedures involved. In this article, we will explore the concept of multiplying fractions and whole numbers, with a focus on the given problem: Multiply. $\frac{4}{5} \times 20$ . We will break down the problem step by step, explaining the reasoning behind each step, and provide examples to illustrate the concept.

Understanding Fractions and Whole Numbers

Before we dive into the problem, let's take a moment to understand the concepts of fractions and whole numbers. 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, $\frac{4}{5}$ is a fraction where 4 is the numerator and 5 is the denominator.

A whole number, on the other hand, is a number that is not a fraction. It is a number that can be expressed without any decimal or fractional part. For example, 20 is a whole number.

Multiplying Fractions and Whole Numbers

When multiplying fractions and whole numbers, we need to follow a specific procedure. The procedure involves multiplying the numerator of the fraction by the whole number, and then multiplying the denominator of the fraction by 1 (since multiplying by 1 does not change the value of the denominator).

Let's apply this procedure to the given problem: Multiply. $\frac{4}{5} \times 20$ . To solve this problem, we need to multiply the numerator (4) by the whole number (20), and then multiply the denominator (5) by 1.

Step-by-Step Solution

Here's the step-by-step solution to the problem:

Multiply the numerator (4) by the whole number (20): 4 × 20 = 80
Multiply the denominator (5) by 1: 5 × 1 = 5
Write the result as a fraction: $\frac{80}{5}$

Simplifying the Fraction

Now that we have the result as a fraction, we need to simplify it. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both numbers by the GCD.

In this case, the GCD of 80 and 5 is 5. So, we can simplify the fraction by dividing both numbers by 5:

$\frac{80}{5} = \frac{80 ÷ 5}{5 ÷ 5} = \frac{16}{1}$

Conclusion

In conclusion, multiplying fractions and whole numbers involves following a specific procedure. We need to multiply the numerator of the fraction by the whole number, and then multiply the denominator of the fraction by 1. The result is a fraction that can be simplified by finding the greatest common divisor (GCD) of the numerator and the denominator, and then dividing both numbers by the GCD.

In this article, we applied this procedure to the given problem: Multiply. $\frac{4}{5} \times 20$ . We broke down the problem step by step, explaining the reasoning behind each step, and provided examples to illustrate the concept.

Examples and Practice Problems

Here are some examples and practice problems to help you practice multiplying fractions and whole numbers:

Multiply. $\frac{3}{4} \times 15$
Multiply. $\frac{2}{3} \times 9$
Multiply. $\frac{5}{6} \times 12$

Tips and Tricks

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

Make sure to multiply the numerator by the whole number, and then multiply the denominator by 1.
Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator, and then dividing both numbers by the GCD.
Practice, practice, practice! The more you practice multiplying fractions and whole numbers, the more comfortable you will become with the procedure.

Common Mistakes to Avoid

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

Don't forget to multiply the numerator by the whole number, and then multiply the denominator by 1.
Don't simplify the fraction by dividing both numbers by a number that is not the greatest common divisor (GCD).
Don't get confused between the numerator and the denominator.

Real-World Applications

Multiplying fractions and whole numbers has many real-world applications. Here are a few examples:

Cooking: When you are cooking, you may need to multiply fractions and whole numbers to measure out ingredients. For example, if a recipe calls for $\frac{1}{4}$ cup of flour and you need to make 4 batches, you would multiply $\frac{1}{4}$ by 4 to get $\frac{1}{1}$ cup of flour.
Science: When you are conducting science experiments, you may need to multiply fractions and whole numbers to measure out chemicals or other substances. For example, if a recipe calls for $\frac{2}{3}$ cup of a certain chemical and you need to make 3 batches, you would multiply $\frac{2}{3}$ by 3 to get $\frac{2}{1}$ cup of the chemical.
Finance: When you are managing your finances, you may need to multiply fractions and whole numbers to calculate interest rates or other financial metrics. For example, if you have a savings account with a 5% interest rate and you want to know how much interest you will earn in a year, you would multiply 5% by 1 to get 5% of the principal amount.

Conclusion

In conclusion, multiplying fractions and whole numbers is an essential skill that has many real-world applications. By following the procedure outlined in this article, you can multiply fractions and whole numbers with confidence. Remember to practice, practice, practice, and don't get confused between the numerator and the denominator. With a little practice, you will become a pro at multiplying fractions and whole numbers!

Introduction

In our previous article, we explored the concept of multiplying fractions and whole numbers, with a focus on the given problem: Multiply. $\frac{4}{5} \times 20$ . We broke down the problem step by step, explaining the reasoning behind each step, and provided examples to illustrate the concept. In this article, we will answer some of the most frequently asked questions (FAQs) related to multiplying fractions and whole numbers.

Q&A

Q1: What is the rule for multiplying fractions and whole numbers?

A1: The rule for multiplying fractions and whole numbers is to multiply the numerator of the fraction by the whole number, and then multiply the denominator of the fraction by 1.

Q2: How do I simplify a fraction after multiplying it by a whole number?

A2: To simplify a fraction after multiplying it by a whole number, you need to find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both numbers by the GCD.

Q3: What is the greatest common divisor (GCD)?

A3: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder.

Q4: How do I find the GCD of two numbers?

A4: To find the GCD of two numbers, you can use the following methods:

List the factors of each number and find the greatest common factor.
Use the Euclidean algorithm to find the GCD.
Use a calculator or online tool to find the GCD.

Q5: What is the difference between a numerator and a denominator?

A5: The numerator is the top number of a fraction, and the denominator is the bottom number of a fraction.

Q6: How do I multiply a fraction by a decimal?

A6: To multiply a fraction by a decimal, you need to convert the decimal to a fraction and then multiply the fractions.

Q7: Can I multiply a fraction by a fraction?

A7: Yes, you can multiply a fraction by a fraction. To do this, you need to multiply the numerators together and multiply the denominators together.

Q8: How do I divide a fraction by a whole number?

A8: To divide a fraction by a whole number, you need to invert the fraction (i.e., flip the numerator and denominator) and then multiply the fraction by the reciprocal of the whole number.

Q9: What is the reciprocal of a fraction?

A9: The reciprocal of a fraction is a fraction with the numerator and denominator swapped.

Q10: How do I convert a fraction to a decimal?

A10: To convert a fraction to a decimal, you need to divide the numerator by the denominator.