Drag The Cards Below To Create An Expression That Is Equal To $\frac{4}{12}$.Cards: 12, 4

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Introduction

When working with fractions, it's essential to understand how to simplify them to their most basic form. This process, known as reducing a fraction, involves dividing both the numerator and the denominator by their greatest common divisor (GCD). In this article, we'll explore how to simplify the fraction $\frac{4}{12}$ using the given cards.

Understanding the Cards

We have two cards with the numbers 12 and 4. Our goal is to create an expression that is equal to $\frac{4}{12}$ using these cards. To do this, we need to understand the concept of equivalent fractions. Equivalent fractions are fractions that have the same value, but with different numerators and denominators.

Creating Equivalent Fractions

To create an equivalent fraction, we can multiply or divide both the numerator and the denominator by the same number. For example, if we have the fraction $\frac{2}{3}$, we can multiply both the numerator and the denominator by 2 to get $\frac{4}{6}$. This new fraction is equivalent to the original fraction.

Simplifying $\frac{4}{12}$

Now, let's apply this concept to the fraction $\frac{4}{12}$. We can see that both the numerator and the denominator have a common factor of 4. To simplify the fraction, we can divide both the numerator and the denominator by 4.

Using the Cards to Simplify the Fraction

Using the cards, we can create the expression $\frac{4}{12}$ by placing the number 4 on top of the number 12. However, we can simplify this fraction further by dividing both the numerator and the denominator by their GCD, which is 4.

Dividing the Numerator and Denominator

To divide the numerator and denominator by 4, we can use the following steps:

1. Divide the numerator (4) by 4: $\frac{4}{4} = 1$
2. Divide the denominator (12) by 4: $\frac{12}{4} = 3$

Simplifying the Fraction

Now that we have divided both the numerator and the denominator by 4, we can simplify the fraction. The simplified fraction is $\frac{1}{3}$.

Conclusion

In this article, we learned how to simplify the fraction $\frac{4}{12}$ using the given cards. We applied the concept of equivalent fractions and divided both the numerator and the denominator by their GCD to simplify the fraction. The simplified fraction is $\frac{1}{3}$.

Frequently Asked Questions

• Q: What is the greatest common divisor (GCD) of 4 and 12? A: The GCD of 4 and 12 is 4.
• Q: How do I simplify a fraction? A: To simplify a fraction, divide both the numerator and the denominator by their GCD.
• Q: What is an equivalent fraction? A: An equivalent fraction is a fraction that has the same value, but with different numerators and denominators.

Additional Resources

• Khan Academy: Simplifying Fractions
• Math Is Fun: Simplifying Fractions
• Purplemath: Simplifying Fractions

Final Thoughts

Simplifying fractions is an essential skill in mathematics. By understanding how to simplify fractions, you can make complex calculations easier and more manageable. In this article, we learned how to simplify the fraction $\frac{4}{12}$ using the given cards. We applied the concept of equivalent fractions and divided both the numerator and the denominator by their GCD to simplify the fraction. The simplified fraction is $\frac{1}{3}$.

Introduction

In our previous article, we explored how to simplify the fraction $\frac{4}{12}$ using the given cards. We applied the concept of equivalent fractions and divided both the numerator and the denominator by their greatest common divisor (GCD) to simplify the fraction. The simplified fraction is $\frac{1}{3}$. In this article, we'll answer some frequently asked questions about simplifying fractions.

Q&A

Q: What is the greatest common divisor (GCD) of 4 and 12?

A: The GCD of 4 and 12 is 4. The GCD is the largest number that divides both numbers without leaving a remainder.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide both the numerator and the denominator by their GCD. This will give you a simplified fraction that has the same value as the original fraction.

Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value as the original fraction, but with different numerators and denominators. For example, $\frac{2}{3}$ and $\frac{4}{6}$ are equivalent fractions.

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

A: To find the GCD of two numbers, you can use the following steps:

1. List the factors of each number.
2. Identify the common factors.
3. Choose the largest common factor.

Q: Can I simplify a fraction with a zero numerator or denominator?

A: No, you cannot simplify a fraction with a zero numerator or denominator. A fraction with a zero numerator or denominator is undefined.

Q: How do I simplify a fraction with a negative numerator or denominator?

A: To simplify a fraction with a negative numerator or denominator, you can follow the same steps as simplifying a fraction with positive numerators and denominators. However, be careful when dividing negative numbers.

Q: Can I simplify a fraction with a decimal numerator or denominator?

A: No, you cannot simplify a fraction with a decimal numerator or denominator. A fraction with a decimal numerator or denominator is not a simplified fraction.

Q: How do I check if a fraction is simplified?

A: To check if a fraction is simplified, you can divide both the numerator and the denominator by their GCD. If the resulting fraction is the same as the original fraction, then the fraction is not simplified.

Q: Can I simplify a fraction with a variable numerator or denominator?

A: Yes, you can simplify a fraction with a variable numerator or denominator. However, be careful when dividing variables.

Conclusion

In this article, we answered some frequently asked questions about simplifying fractions. We covered topics such as the greatest common divisor, equivalent fractions, and simplifying fractions with negative or decimal numerators and denominators. We also provided steps for finding the GCD of two numbers and checking if a fraction is simplified.

Frequently Asked Questions

• Q: What is the greatest common divisor (GCD) of 4 and 12? A: The GCD of 4 and 12 is 4.
• Q: How do I simplify a fraction? A: To simplify a fraction, divide both the numerator and the denominator by their GCD.
• Q: What is an equivalent fraction? A: An equivalent fraction is a fraction that has the same value as the original fraction, but with different numerators and denominators.

Additional Resources

• Khan Academy: Simplifying Fractions
• Math Is Fun: Simplifying Fractions
• Purplemath: Simplifying Fractions

Final Thoughts

Simplifying fractions is an essential skill in mathematics. By understanding how to simplify fractions, you can make complex calculations easier and more manageable. In this article, we answered some frequently asked questions about simplifying fractions and provided steps for finding the GCD of two numbers and checking if a fraction is simplified.