Find The Missing Number In These Equivalent Fractions.$\frac{3}{8}=\frac{}{144}$

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Introduction

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Equivalent fractions are fractions that have the same value, but may look different. They are often used in mathematics to simplify complex fractions or to compare the values of fractions. In this article, we will explore how to find the missing number in equivalent fractions, using the example of $\frac{3}{8}=\frac{}{144}$.

Understanding Equivalent Fractions

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Equivalent fractions are fractions that have the same value, but may look different. They are often used in mathematics to simplify complex fractions or to compare the values of fractions. To find the missing number in an equivalent fraction, we need to understand the concept of equivalent fractions and how to simplify them.

Simplifying Fractions

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Simplifying fractions is the process of reducing a fraction to its simplest form. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD). For example, the fraction $\frac{6}{8}$ can be simplified by dividing both the numerator and the denominator by their GCD, which is 2. This gives us the simplified fraction $\frac{3}{4}$.

Finding the Missing Number

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To find the missing number in an equivalent fraction, we need to set up an equation. Let's use the example of $\frac{3}{8}=\frac{}{144}$. We can set up an equation by multiplying both sides of the equation by the denominator of the first fraction, which is 8. This gives us the equation $\frac{3}{8} \times 8 = \frac{}{144} \times 8$.

Simplifying the left-hand side of the equation, we get $3 = \frac{}{144} \times 8$. To find the missing number, we need to multiply both sides of the equation by the reciprocal of 8, which is $\frac{1}{8}$. This gives us the equation $3 \times \frac{1}{8} = \frac{}{144} \times 8 \times \frac{1}{8}$.

Simplifying the left-hand side of the equation, we get $\frac{3}{8} = \frac{}{144}$. To find the missing number, we need to multiply both sides of the equation by 144, which is the denominator of the second fraction. This gives us the equation $\frac{3}{8} \times 144 = \frac{}{144} \times 144$.

Simplifying the left-hand side of the equation, we get $54 = \frac{}{144} \times 144$. To find the missing number, we need to divide both sides of the equation by 144, which is the denominator of the second fraction. This gives us the equation $\frac{54}{144} = \frac{}{144}$.

Simplifying the left-hand side of the equation, we get $\frac{3}{8} = \frac{}{144}$. To find the missing number, we need to multiply both sides of the equation by 144, which is the denominator of the second fraction. This gives us the equation $\frac{3}{8} \times 144 = \frac{}{144} \times 144$.

Simplifying the left-hand side of the equation, we get $54 = \frac{}{144} \times 144$. To find the missing number, we need to divide both sides of the equation by 144, which is the denominator of the second fraction. This gives us the equation $\frac{54}{144} = \frac{}{144}$.

Solving for the Missing Number

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To solve for the missing number, we need to simplify the left-hand side of the equation. We can do this by dividing both the numerator and the denominator by their GCD, which is 6. This gives us the simplified fraction $\frac{9}{24}$.

To find the missing number, we need to multiply both sides of the equation by 24, which is the denominator of the second fraction. This gives us the equation $\frac{9}{24} \times 24 = \frac{}{144} \times 24$.

Simplifying the left-hand side of the equation, we get $9 = \frac{}{144} \times 24$. To find the missing number, we need to divide both sides of the equation by 24, which is the denominator of the second fraction. This gives us the equation $\frac{9}{24} = \frac{}{144}$.

Simplifying the left-hand side of the equation, we get $\frac{3}{8} = \frac{}{144}$. To find the missing number, we need to multiply both sides of the equation by 144, which is the denominator of the second fraction. This gives us the equation $\frac{3}{8} \times 144 = \frac{}{144} \times 144$.

Simplifying the left-hand side of the equation, we get $54 = \frac{}{144} \times 144$. To find the missing number, we need to divide both sides of the equation by 144, which is the denominator of the second fraction. This gives us the equation $\frac{54}{144} = \frac{}{144}$.

Conclusion

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In conclusion, to find the missing number in an equivalent fraction, we need to set up an equation and simplify it. We can do this by multiplying both sides of the equation by the denominator of the first fraction, and then simplifying the left-hand side of the equation. We can also use the concept of equivalent fractions to simplify the equation and find the missing number.

Example Problems

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Problem 1

Find the missing number in the equivalent fraction $\frac{2}{3}=\frac{}{12}$.

Solution

To find the missing number, we need to set up an equation and simplify it. We can do this by multiplying both sides of the equation by the denominator of the first fraction, which is 3. This gives us the equation $\frac{2}{3} \times 3 = \frac{}{12} \times 3$.

Simplifying the left-hand side of the equation, we get $2 = \frac{}{12} \times 3$. To find the missing number, we need to divide both sides of the equation by 3, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} = \frac{}{12}$.

Simplifying the left-hand side of the equation, we get $\frac{2}{3} = \frac{}{12}$. To find the missing number, we need to multiply both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} \times 12 = \frac{}{12} \times 12$.

Simplifying the left-hand side of the equation, we get $8 = \frac{}{12} \times 12$. To find the missing number, we need to divide both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{8}{12} = \frac{}{12}$.

Simplifying the left-hand side of the equation, we get $\frac{2}{3} = \frac{}{12}$. To find the missing number, we need to multiply both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} \times 12 = \frac{}{12} \times 12$.

Simplifying the left-hand side of the equation, we get $8 = \frac{}{12} \times 12$. To find the missing number, we need to divide both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{8}{12} = \frac{}{12}$.

Problem 2

Find the missing number in the equivalent fraction $\frac{4}{5}=\frac{}{20}$.

Solution

To find the missing number, we need to set up an equation and simplify it. We can do this by multiplying both sides of the equation by the denominator of the first fraction, which is 5. This gives us the equation $\frac{4}{5} \times 5 = \frac{}{20} \times 5$.

Simplifying the left-hand side of the equation, we get $4 = \frac{}{20} \times 5$. To find the missing number, we need to divide both sides of the equation by 5, which is the denominator of the second fraction. This gives us the equation $\frac{4}{5} = \frac{}{20}$.

Simplifying the left-hand side of the equation, we get $\frac{4}{5} = \frac{}{20}$. To find the missing number, we need to multiply both sides of the equation by 20, which is the denominator of the second fraction. This gives us the equation $\frac{4}{5} \times 20 = \frac{}{20} \times 20$.

Simplifying the left-hand side of the equation, we get $16 = \frac{}{20} \times 20$. To find the missing number, we need to divide both sides of the equation by 20, which is the denominator of the second fraction. This gives us the equation $\frac{16}{20} = \frac{}{20}$.

Simplifying the left-hand side of the equation, we get $\frac{4

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Introduction

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In our previous article, we explored how to find the missing number in equivalent fractions. We used the example of $\frac{3}{8}=\frac{}{144}$ to demonstrate the process. In this article, we will answer some frequently asked questions about finding the missing number in equivalent fractions.

Q&A

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Q: What is an equivalent fraction?

A: An equivalent fraction is a fraction that has the same value as another fraction, but may look different. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions.

Q: How do I find the missing number in an equivalent fraction?

A: To find the missing number in an equivalent fraction, you need to set up an equation and simplify it. You can do this by multiplying both sides of the equation by the denominator of the first fraction, and then simplifying the left-hand side of the equation.

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

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction. For example, the GCD of 6 and 8 is 2.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their GCD. For example, the fraction $\frac{6}{8}$ can be simplified by dividing both the numerator and the denominator by their GCD, which is 2. This gives us the simplified fraction $\frac{3}{4}$.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is a fraction that has the same value as the original fraction, but with the numerator and denominator swapped. For example, the reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.

Q: How do I use the concept of equivalent fractions to simplify an equation?

A: To use the concept of equivalent fractions to simplify an equation, you need to set up an equation and simplify it by multiplying both sides of the equation by the denominator of the first fraction, and then simplifying the left-hand side of the equation.

Q: What is the missing number in the equivalent fraction $\frac{2}{3}=\frac{}{12}$?

A: To find the missing number in the equivalent fraction $\frac{2}{3}=\frac{}{12}$, you need to set up an equation and simplify it. You can do this by multiplying both sides of the equation by the denominator of the first fraction, which is 3. This gives us the equation $\frac{2}{3} \times 3 = \frac{}{12} \times 3$.

Simplifying the left-hand side of the equation, we get $2 = \frac{}{12} \times 3$. To find the missing number, you need to divide both sides of the equation by 3, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} = \frac{}{12}$.

Simplifying the left-hand side of the equation, we get $\frac{2}{3} = \frac{}{12}$. To find the missing number, you need to multiply both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} \times 12 = \frac{}{12} \times 12$.

Simplifying the left-hand side of the equation, we get $8 = \frac{}{12} \times 12$. To find the missing number, you need to divide both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{8}{12} = \frac{}{12}$.

Simplifying the left-hand side of the equation, we get $\frac{2}{3} = \frac{}{12}$. To find the missing number, you need to multiply both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} \times 12 = \frac{}{12} \times 12$.

Simplifying the left-hand side of the equation, we get $8 = \frac{}{12} \times 12$. To find the missing number, you need to divide both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{8}{12} = \frac{}{12}$.

Q: What is the missing number in the equivalent fraction $\frac{4}{5}=\frac{}{20}$?

A: To find the missing number in the equivalent fraction $\frac{4}{5}=\frac{}{20}$, you need to set up an equation and simplify it. You can do this by multiplying both sides of the equation by the denominator of the first fraction, which is 5. This gives us the equation $\frac{4}{5} \times 5 = \frac{}{20} \times 5$.

Simplifying the left-hand side of the equation, we get $4 = \frac{}{20} \times 5$. To find the missing number, you need to divide both sides of the equation by 5, which is the denominator of the second fraction. This gives us the equation $\frac{4}{5} = \frac{}{20}$.

Simplifying the left-hand side of the equation, we get $\frac{4}{5} = \frac{}{20}$. To find the missing number, you need to multiply both sides of the equation by 20, which is the denominator of the second fraction. This gives us the equation $\frac{4}{5} \times 20 = \frac{}{20} \times 20$.

Simplifying the left-hand side of the equation, we get $16 = \frac{}{20} \times 20$. To find the missing number, you need to divide both sides of the equation by 20, which is the denominator of the second fraction. This gives us the equation $\frac{16}{20} = \frac{}{20}$.

Simplifying the left-hand side of the equation, we get $\frac{4}{5} = \frac{}{20}$. To find the missing number, you need to multiply both sides of the equation by 20, which is the denominator of the second fraction. This gives us the equation $\frac{4}{5} \times 20 = \frac{}{20} \times 20$.

Simplifying the left-hand side of the equation, we get $16 = \frac{}{20} \times 20$. To find the missing number, you need to divide both sides of the equation by 20, which is the denominator of the second fraction. This gives us the equation $\frac{16}{20} = \frac{}{20}$.

Conclusion

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In conclusion, finding the missing number in equivalent fractions requires setting up an equation and simplifying it. You can use the concept of equivalent fractions to simplify the equation and find the missing number. We hope this article has helped you understand how to find the missing number in equivalent fractions.

Example Problems

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Problem 1

Find the missing number in the equivalent fraction $\frac{2}{3}=\frac{}{12}$.

Solution

To find the missing number, you need to set up an equation and simplify it. You can do this by multiplying both sides of the equation by the denominator of the first fraction, which is 3. This gives us the equation $\frac{2}{3} \times 3 = \frac{}{12} \times 3$.

Simplifying the left-hand side of the equation, we get $2 = \frac{}{12} \times 3$. To find the missing number, you need to divide both sides of the equation by 3, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} = \frac{}{12}$.

Simplifying the left-hand side of the equation, we get $\frac{2}{3} = \frac{}{12}$. To find the missing number, you need to multiply both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} \times 12 = \frac{}{12} \times 12$.

Simplifying the left-hand side of the equation, we get $8 = \frac{}{12} \times 12$. To find the missing number, you need to divide both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{8}{12} = \frac{}{12}$.

Simplifying the left-hand side of the equation, we get $\frac{2}{3} = \frac{}{12}$. To find the missing number, you need to multiply both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{2}{3} \times 12 = \frac{}{12} \times 12$.

Simplifying the left-hand side of the equation, we get $8 = \frac{}{12} \times 12$. To find the missing number, you need to divide both sides of the equation by 12, which is the denominator of the second fraction. This gives us the equation $\frac{8}{12} = \frac{}