Determine If The Fractions Are Equivalent:$\[ \frac{5}{6} = \frac{15}{18} \\]

Introduction

In mathematics, equivalent fractions are fractions that have the same value, even though they may look different. To determine if two fractions are equivalent, we need to compare their values. In this article, we will learn how to determine if the fractions $\frac{5}{6}$ and $\frac{15}{18}$ are equivalent.

What are Equivalent Fractions?

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

How to Determine if Fractions are Equivalent

To determine if two fractions are equivalent, we need to compare their values. We can do this by cross-multiplying the fractions, which means multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

Cross-Multiplying Fractions

Cross-multiplying fractions is a simple process that involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa. For example, to cross-multiply the fractions $\frac{5}{6}$ and $\frac{15}{18}$, we would multiply the numerator of the first fraction (5) by the denominator of the second fraction (18), and vice versa.

Example: Cross-Multiplying $\frac{5}{6}$ and $\frac{15}{18}$

To cross-multiply the fractions $\frac{5}{6}$ and $\frac{15}{18}$, we would multiply the numerator of the first fraction (5) by the denominator of the second fraction (18), and vice versa.

5 × 18 = 90 15 × 6 = 90

As we can see, the products of the cross-multiplication are equal, which means that the fractions $\frac{5}{6}$ and $\frac{15}{18}$ are equivalent.

Why are Equivalent Fractions Important?

Equivalent fractions are important in mathematics because they allow us to simplify complex fractions and make them easier to work with. For example, if we have a fraction that is difficult to simplify, we can try to find an equivalent fraction that is easier to work with.

Real-World Applications of Equivalent Fractions

Equivalent fractions have many real-world applications. For example, in cooking, we may need to measure out a certain amount of ingredients, but we may not have the exact amount we need. In this case, we can use equivalent fractions to simplify the measurement and make it easier to work with.

Conclusion

In conclusion, equivalent fractions are fractions that have the same value, even though they may look different. To determine if two fractions are equivalent, we need to compare their values by cross-multiplying the fractions. We have seen that the fractions $\frac{5}{6}$ and $\frac{15}{18}$ are equivalent because the products of the cross-multiplication are equal. Equivalent fractions are important in mathematics because they allow us to simplify complex fractions and make them easier to work with.

Frequently Asked Questions

Q: What are equivalent fractions?

A: Equivalent fractions are fractions that have the same value, even though they may look different.

Q: How do I determine if two fractions are equivalent?

A: To determine if two fractions are equivalent, you need to compare their values by cross-multiplying the fractions.

Q: What is cross-multiplication?

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

Q: Why are equivalent fractions important?

A: Equivalent fractions are important in mathematics because they allow us to simplify complex fractions and make them easier to work with.

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

A: Equivalent fractions have many real-world applications, such as in cooking and measurement.

Glossary of Terms

Equivalent Fractions

Fractions that have the same value, even though they may look different.

Cross-Multiplication

A process that involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

Numerator

The number on top of a fraction.

Denominator

The number on the bottom of a fraction.

Fraction

A way of expressing a part of a whole as a ratio of two numbers.

References

• [1] "Equivalent Fractions" by Math Open Reference. Retrieved from https://www.mathopenref.com/equivalentfractions.html
• [2] "Cross-Multiplication" by Khan Academy. Retrieved from <https://www.khanacademy.org/math/algebra/x2f6f7c0b-9b7a-4a3f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8a4f-8
  Frequently Asked Questions: Equivalent Fractions =====================================================

Q: What are equivalent fractions?

A: Equivalent fractions are fractions that have the same value, even though they may look different. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions because they have the same value.

Q: How do I determine if two fractions are equivalent?

A: To determine if two fractions are equivalent, you need to compare their values by cross-multiplying the fractions. This involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

Q: What is cross-multiplication?

A: Cross-multiplication is a process that involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa. For example, to cross-multiply the fractions $\frac{5}{6}$ and $\frac{15}{18}$, we would multiply the numerator of the first fraction (5) by the denominator of the second fraction (18), and vice versa.

Q: Why are equivalent fractions important?

A: Equivalent fractions are important in mathematics because they allow us to simplify complex fractions and make them easier to work with. For example, if we have a fraction that is difficult to simplify, we can try to find an equivalent fraction that is easier to work with.

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

A: Equivalent fractions have many real-world applications, such as in cooking and measurement. For example, if we need to measure out a certain amount of ingredients, but we don't have the exact amount we need, we can use equivalent fractions to simplify the measurement and make it easier to work with.

Q: Can you give me an example of how to use equivalent fractions in a real-world situation?

A: Let's say we need to make a recipe that calls for 1/4 cup of sugar, but we only have a 1/2 cup measuring cup. We can use equivalent fractions to find out how much sugar we need to measure out. Since 1/4 is equivalent to 2/8, we can measure out 2/8 of the sugar using the 1/2 cup measuring cup.

Q: How do I simplify a fraction using equivalent fractions?

A: To simplify a fraction using equivalent fractions, you need to find an equivalent fraction that has a smaller numerator and denominator. For example, if we have the fraction $\frac{12}{16}$, we can simplify it by finding an equivalent fraction with a smaller numerator and denominator. Since 12 is equivalent to 3 × 4, and 16 is equivalent to 4 × 4, we can simplify the fraction to $\frac{3}{4}$.

Q: Can you give me an example of how to simplify a fraction using equivalent fractions?

A: Let's say we have the fraction $\frac{12}{16}$. We can simplify it by finding an equivalent fraction with a smaller numerator and denominator. Since 12 is equivalent to 3 × 4, and 16 is equivalent to 4 × 4, we can simplify the fraction to $\frac{3}{4}$.

Q: How do I add or subtract fractions using equivalent fractions?

A: To add or subtract fractions using equivalent fractions, you need to find a common denominator for the fractions. Once you have a common denominator, you can add or subtract the numerators of the fractions.

Q: Can you give me an example of how to add fractions using equivalent fractions?

A: Let's say we have the fractions $\frac{1}{4}$ and $\frac{1}{6}$. We can add them by finding a common denominator, which is 12. Since $\frac{1}{4}$ is equivalent to $\frac{3}{12}$, and $\frac{1}{6}$ is equivalent to $\frac{2}{12}$, we can add the fractions to get $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$.

Q: How do I multiply fractions using equivalent fractions?

A: To multiply fractions using equivalent fractions, you need to multiply the numerators of the fractions and multiply the denominators of the fractions.

Q: Can you give me an example of how to multiply fractions using equivalent fractions?

A: Let's say we have the fractions $\frac{1}{2}$ and $\frac{3}{4}$. We can multiply them by multiplying the numerators (1 × 3 = 3) and multiplying the denominators (2 × 4 = 8). The result is $\frac{3}{8}$.

Q: Can you give me a list of common equivalent fractions?

A: Here are some common equivalent fractions:

• $\frac{1}{2}$ and $\frac{2}{4}$
• $\frac{1}{3}$ and $\frac{2}{6}$
• $\frac{1}{4}$ and $\frac{2}{8}$
• $\frac{1}{5}$ and $\frac{2}{10}$
• $\frac{1}{6}$ and $\frac{2}{12}$

Q: How do I find equivalent fractions?

A: To find equivalent fractions, you need to multiply or divide the numerator and denominator of the fraction by the same number. For example, to find an equivalent fraction of $\frac{1}{2}$, you can multiply the numerator and denominator by 2 to get $\frac{2}{4}$.

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

A: Let's say we have the fraction $\frac{1}{2}$. We can find an equivalent fraction by multiplying the numerator and denominator by 2 to get $\frac{2}{4}$.

Q: How do I use equivalent fractions in algebra?

A: Equivalent fractions can be used in algebra to simplify complex fractions and make them easier to work with. For example, if we have a fraction that is difficult to simplify, we can try to find an equivalent fraction that is easier to work with.

Q: Can you give me an example of how to use equivalent fractions in algebra?

A: Let's say we have the fraction $\frac{12}{16}$. We can simplify it by finding an equivalent fraction with a smaller numerator and denominator. Since 12 is equivalent to 3 × 4, and 16 is equivalent to 4 × 4, we can simplify the fraction to $\frac{3}{4}$.

Q: How do I use equivalent fractions in geometry?

A: Equivalent fractions can be used in geometry to simplify complex fractions and make them easier to work with. For example, if we have a fraction that is difficult to simplify, we can try to find an equivalent fraction that is easier to work with.

Q: Can you give me an example of how to use equivalent fractions in geometry?

A: Let's say we have the fraction $\frac{1}{2}$. We can use it to find the area of a circle with a radius of 2. Since the area of a circle is given by the formula $A = \pi r^2$, we can substitute the value of $r$ to get $A = \pi (2)^2 = 4\pi$. We can simplify this expression by finding an equivalent fraction with a smaller numerator and denominator. Since 4 is equivalent to 2 × 2, and $\pi$ is equivalent to $\frac{22}{7}$, we can simplify the expression to $\frac{44}{7}$.

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

A: Equivalent fractions can be used in real-world applications to simplify complex fractions and make them easier to work with. For example, if we need to measure out a certain amount of ingredients, but we don't have the exact amount we need, we can use equivalent fractions to simplify the measurement and make it easier to work with.

Q: Can you give me an example of how to use equivalent fractions in real-world applications?

A: Let's say we need to make a recipe that calls for 1/4 cup of sugar, but we only have a 1/2 cup measuring cup. We can use equivalent fractions to find out how much sugar we need to measure out. Since 1/4 is equivalent to 2/8, we can measure out 2/8 of the sugar using the 1/2 cup measuring cup.

Q: How do I use equivalent fractions in finance?

A: Equivalent fractions can be used in finance to simplify complex fractions and make them easier to work with. For example, if we need to calculate the interest on a loan, but we don't have the exact amount we need, we can use equivalent fractions to simplify the calculation and make it easier to work with.

Q: Can you give me an example of how to use equivalent fractions in finance?

A: Let's say we have a loan of $1000 with an interest rate of 5%. We can calculate the interest on the loan by multiplying the principal amount by the interest rate. Since the interest rate is 5%, we can multiply the principal amount by 0.05 to get $50. We can simplify this expression by finding an equivalent fraction with a smaller numerator and denominator. Since 50 is equivalent to 10 × 5, and 1000 is equivalent to 10 × 100, we can simplify the expression to $\frac{1}{20}$.

**Q: How do I use equivalent