Use the least common multiple

Oct 13, 2025 by miodeya.com 45 views

Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, even though they may look different. In other words, two fractions are equivalent if they can be simplified to the same ratio. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they both represent the same amount of a whole.

The Problem: $\frac{3}{4}=\frac{?}{20}$

We are given the equivalent fraction $\frac{3}{4}$ and asked to find the missing numerator that completes the pattern. To solve this problem, we need to find a fraction that has the same value as $\frac{3}{4}$ , but with a denominator of 20.

Step 1: Identify the Relationship Between the Denominators

The original fraction has a denominator of 4, and we want to find a fraction with a denominator of 20. To do this, we need to find a common multiple of 4 and 20. The least common multiple (LCM) of 4 and 20 is 20.

Step 2: Find the Missing Numerator

Since the LCM of 4 and 20 is 20, we can multiply the numerator and denominator of the original fraction by 5 to get a fraction with a denominator of 20. This gives us:

\frac{3}{4} \times \frac{5}{5} = \frac{15}{20}

Therefore, the missing numerator that completes the pattern of equivalent fractions is 15.

Conclusion

In this article, we solved the problem of finding the missing numerator that completes the pattern of equivalent fractions. We identified the relationship between the denominators, found the least common multiple, and multiplied the numerator and denominator of the original fraction to get the missing numerator. The final answer is $\boxed{15}$ .

Why is this Important?

Understanding equivalent fractions is an important concept in mathematics, as it allows us to compare and simplify fractions. This concept is used in a variety of real-world applications, such as cooking, finance, and science.

Real-World Applications

Equivalent fractions are used in a variety of real-world applications, such as:

Cooking: When a recipe calls for a certain amount of an ingredient, equivalent fractions can be used to scale up or down the recipe.
Finance: Equivalent fractions can be used to compare interest rates and investment returns.
Science: Equivalent fractions can be used to compare the concentrations of solutions and mixtures.

Tips and Tricks

Here are some tips and tricks for working with equivalent fractions:

Use the least common multiple: When working with equivalent fractions, it's often helpful to use the least common multiple of the denominators.
Multiply the numerator and denominator: To find an equivalent fraction, multiply the numerator and denominator of the original fraction by the same number.
Simplify the fraction: Once you've found an equivalent fraction, simplify it by dividing both the numerator and denominator by their greatest common divisor.

Common Mistakes

Here are some common mistakes to avoid when working with equivalent fractions:

Not using the least common multiple: Failing to use the least common multiple can lead to incorrect answers.
Not multiplying the numerator and denominator: Failing to multiply the numerator and denominator can lead to incorrect answers.
Not simplifying the fraction: Failing to simplify the fraction can lead to incorrect answers.

Conclusion

Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value as another fraction, but with different numerators and denominators.

Q: How do I find an equivalent fraction?

A: To find an equivalent fraction, you can multiply the numerator and denominator of the original fraction by the same number. This will give you a new fraction that has the same value as the original fraction.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. In the context of equivalent fractions, the LCM is used to find the common denominator of two fractions.

Q: How do I use the LCM to find an equivalent fraction?

A: To use the LCM to find an equivalent fraction, you can multiply the numerator and denominator of the original fraction by the LCM. This will give you a new fraction that has the same value as the original fraction.

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

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. In the context of equivalent fractions, the GCD is used to simplify a fraction.

Q: How do I simplify a fraction?

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

Q: What is the difference between equivalent fractions and similar fractions?

A: Equivalent fractions are fractions that have the same value, but with different numerators and denominators. Similar fractions are fractions that have the same numerator and denominator, but with different values.

Q: Can you give me an example of equivalent fractions?

A: Yes, here is an example of equivalent fractions:

$\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they both represent the same amount of a whole.

Q: Can you give me an example of similar fractions?

A: Yes, here is an example of similar fractions:

$\frac{1}{2}$ and $\frac{3}{6}$ are similar fractions because they have the same numerator and denominator, but with different values.

Q: How do I use equivalent fractions in real-life situations?

A: Equivalent fractions can be used in a variety of real-life situations, such as:

Cooking: When a recipe calls for a certain amount of an ingredient, equivalent fractions can be used to scale up or down the recipe.
Finance: Equivalent fractions can be used to compare interest rates and investment returns.
Science: Equivalent fractions can be used to compare the concentrations of solutions and mixtures.

Q: What are some common mistakes to avoid when working with equivalent fractions?

A: Some common mistakes to avoid when working with equivalent fractions include:

Not using the least common multiple: Failing to use the least common multiple can lead to incorrect answers.
Not multiplying the numerator and denominator: Failing to multiply the numerator and denominator can lead to incorrect answers.
Not simplifying the fraction: Failing to simplify the fraction can lead to incorrect answers.

Q: How can I practice working with equivalent fractions?

A: You can practice working with equivalent fractions by:

Using online resources: There are many online resources available that provide practice problems and exercises for working with equivalent fractions.
Working with a tutor: A tutor can provide one-on-one instruction and practice with equivalent fractions.
Using real-life examples: Using real-life examples can help you see how equivalent fractions are used in everyday situations.