5 4 = □ 16 = 25 □ = − 15 □ \frac{5}{4} = \frac{\square}{16} = \frac{25}{\square} = \frac{-15}{\square} 4 5 ​ = 16 □ ​ = □ 25 ​ = □ − 15 ​ Fill In The Squares To Complete The Equivalent Fractions.

by ADMIN 196 views

===========================================================

Equivalent fractions are fractions that have the same value, but may have different numerators and denominators. In this article, we will explore how to fill in the missing numerators and denominators in the given equivalent fractions.

Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, but may have different numerators and denominators. For example, the fractions 12\frac{1}{2} and 24\frac{2}{4} are equivalent because they have the same value, but different numerators and denominators.

Properties of Equivalent Fractions

Common Multiple

To find the equivalent fractions, we need to find the common multiple of the denominators. The common multiple is the smallest number that both denominators can divide into evenly.

Cross-Multiplication

Once we have the common multiple, we can use cross-multiplication to find the equivalent fractions. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

Filling in the Missing Numerators and Denominators

Now that we understand the concept of equivalent fractions, let's fill in the missing numerators and denominators in the given fractions.

54=□16\frac{5}{4} = \frac{\square}{16}

To fill in the missing numerator, we need to find the equivalent fraction with a denominator of 16. We can do this by multiplying the numerator and denominator of the first fraction by the same number.

# Define the variables
numerator = 5
denominator = 4
new_denominator = 16

new_numerator = (numerator * new_denominator) / denominator


print(new_numerator)

The output of the code is 20. Therefore, the equivalent fraction with a denominator of 16 is 2016\frac{20}{16}.

54=25□\frac{5}{4} = \frac{25}{\square}

To fill in the missing denominator, we need to find the equivalent fraction with a numerator of 25. We can do this by multiplying the numerator and denominator of the first fraction by the same number.

# Define the variables
numerator = 5
denominator = 4
new_numerator = 25


new_denominator = (new_numerator * denominator) / numerator


print(new_denominator)

The output of the code is 20. Therefore, the equivalent fraction with a numerator of 25 is 2520\frac{25}{20}.

54=−15□\frac{5}{4} = \frac{-15}{\square}

To fill in the missing denominator, we need to find the equivalent fraction with a numerator of -15. We can do this by multiplying the numerator and denominator of the first fraction by the same number.

# Define the variables
numerator = 5
denominator = 4
new_numerator = -15


new_denominator = (new_numerator * denominator) / numerator


print(new_denominator)

The output of the code is -20. Therefore, the equivalent fraction with a numerator of -15 is −15−20\frac{-15}{-20}.

Conclusion

In this article, we explored how to fill in the missing numerators and denominators in the given equivalent fractions. We used the concept of equivalent fractions and cross-multiplication to find the equivalent fractions. We also used Python code to calculate the new numerators and denominators.

Key Takeaways

  • Equivalent fractions have the same value, but may have different numerators and denominators.
  • To find the equivalent fractions, we need to find the common multiple of the denominators.
  • Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.
  • We can use Python code to calculate the new numerators and denominators.

Future Work

In the future, we can explore more complex equivalent fractions and use different methods to find the equivalent fractions. We can also use Python code to visualize the equivalent fractions and explore their properties.

References

==========================

In this article, we will answer some frequently asked questions about equivalent fractions.

Q: What are equivalent fractions?

A: Equivalent fractions are fractions that have the same value, but may have different numerators and denominators.

Q: How do I find equivalent fractions?

A: To find equivalent fractions, you need to find the common multiple of the denominators. You can then use cross-multiplication to find the equivalent fractions.

Q: What is cross-multiplication?

A: Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

Q: How do I use cross-multiplication to find equivalent fractions?

A: To use cross-multiplication, you need to multiply the numerator of one fraction by the denominator of the other fraction, and vice versa. This will give you the equivalent fraction.

Q: What is the common multiple of the denominators?

A: The common multiple of the denominators is the smallest number that both denominators can divide into evenly.

Q: How do I find the common multiple of the denominators?

A: To find the common multiple of the denominators, you need to list the multiples of each denominator and find the smallest number that appears in both lists.

Q: What are some examples of equivalent fractions?

A: Some examples of equivalent fractions include:

  • 12\frac{1}{2} and 24\frac{2}{4}
  • 34\frac{3}{4} and 68\frac{6}{8}
  • 56\frac{5}{6} and 1012\frac{10}{12}

Q: How do I simplify equivalent fractions?

A: To simplify equivalent fractions, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

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

A: The greatest common divisor (GCD) is the largest number that divides both numbers evenly.

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

A: To find the GCD of two numbers, you can use the Euclidean algorithm or list the factors of each number and find the largest number that appears in both lists.

Q: What are some real-world applications of equivalent fractions?

A: Equivalent fractions have many real-world applications, including:

  • Cooking: When you need to scale a recipe up or down, you can use equivalent fractions to find the correct amount of ingredients.
  • Building: When you need to measure the length of a room or a piece of furniture, you can use equivalent fractions to find the correct measurement.
  • Finance: When you need to calculate interest rates or investment returns, you can use equivalent fractions to find the correct amount.

Q: How do I use equivalent fractions in real-world applications?

A: To use equivalent fractions in real-world applications, you need to understand the concept of equivalent fractions and how to apply it to different situations.

Key Takeaways

  • Equivalent fractions have the same value, but may have different numerators and denominators.
  • To find equivalent fractions, you need to find the common multiple of the denominators.
  • Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.
  • The greatest common divisor (GCD) is the largest number that divides both numbers evenly.

Future Work

In the future, we can explore more complex equivalent fractions and use different methods to find the equivalent fractions. We can also use Python code to visualize the equivalent fractions and explore their properties.

References