Rewrite The Proportion 7:21 = 3:9 As A Proportion Using Fractions.A) $\frac{7}{21} = \frac{3}{9}$B) $\frac{21}{7} = \frac{3}{9}$C) $\frac{7}{21} = \frac{9}{3}$D) $\frac{7}{9} = \frac{3}{21}$

Understanding Proportions and Fractions

In mathematics, a proportion is a statement that two ratios are equal. It is often expressed as a fraction, where the ratio of two quantities is equal to the ratio of two other quantities. Fractions are a way of representing a part of a whole, and they are used extensively in mathematics to solve problems and represent relationships between quantities.

Rewriting the Proportion 7:21 = 3:9

To rewrite the proportion 7:21 = 3:9 as a proportion using fractions, we need to express each ratio as a fraction. A ratio is a comparison of two quantities, and it can be expressed as a fraction by dividing the first quantity by the second quantity.

Option A: $\frac{7}{21} = \frac{3}{9}$

Option A is a correct representation of the proportion 7:21 = 3:9 as a fraction. The ratio 7:21 is expressed as the fraction $\frac{7}{21}$, and the ratio 3:9 is expressed as the fraction $\frac{3}{9}$. Since the two fractions are equal, this option is a correct representation of the proportion.

Option B: $\frac{21}{7} = \frac{3}{9}$

Option B is not a correct representation of the proportion 7:21 = 3:9 as a fraction. The ratio 7:21 is expressed as the fraction $\frac{21}{7}$, which is the reciprocal of the original ratio. The ratio 3:9 is still expressed as the fraction $\frac{3}{9}$. Since the two fractions are not equal, this option is not a correct representation of the proportion.

Option C: $\frac{7}{21} = \frac{9}{3}$

Option C is not a correct representation of the proportion 7:21 = 3:9 as a fraction. The ratio 7:21 is expressed as the fraction $\frac{7}{21}$, which is the original ratio. The ratio 3:9 is expressed as the fraction $\frac{9}{3}$, which is the reciprocal of the original ratio. Since the two fractions are not equal, this option is not a correct representation of the proportion.

Option D: $\frac{7}{9} = \frac{3}{21}$

Option D is not a correct representation of the proportion 7:21 = 3:9 as a fraction. The ratio 7:21 is expressed as the fraction $\frac{7}{9}$, which is not the original ratio. The ratio 3:9 is expressed as the fraction $\frac{3}{21}$, which is not the original ratio. Since the two fractions are not equal, this option is not a correct representation of the proportion.

Conclusion

In conclusion, the correct representation of the proportion 7:21 = 3:9 as a fraction is option A: $\frac{7}{21} = \frac{3}{9}$. This option correctly expresses each ratio as a fraction and shows that the two ratios are equal.

Understanding Fractions and Proportions

Fractions and proportions are fundamental concepts in mathematics that are used extensively in problem-solving and mathematical modeling. Understanding fractions and proportions is essential for solving problems in mathematics, science, and engineering.

Types of Fractions

There are several types of fractions, including:

• Proper fractions: A fraction where the numerator is less than the denominator, such as $\frac{1}{2}$.
• Improper fractions: A fraction where the numerator is greater than or equal to the denominator, such as $\frac{3}{2}$.
• Mixed numbers: A combination of a whole number and a proper fraction, such as $2\frac{1}{2}$.
• Equivalent fractions: Fractions that have the same value, such as $\frac{1}{2}$ and $\frac{2}{4}$.

Simplifying Fractions

Simplifying fractions is an essential skill in mathematics that involves reducing a fraction to its simplest form. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Example

Suppose we want to simplify the fraction $\frac{12}{18}$. To do this, we need to find the GCD of 12 and 18, which is 6. We can then divide both numbers by 6 to get the simplified fraction: $\frac{12}{18} = \frac{2}{3}$.

Real-World Applications of Fractions and Proportions

Fractions and proportions have numerous real-world applications in mathematics, science, and engineering. Some examples include:

• Cooking: Fractions and proportions are used extensively in cooking to measure ingredients and scale recipes.
• Building design: Fractions and proportions are used in building design to create scale models and calculate materials.
• Physics: Fractions and proportions are used in physics to describe the motion of objects and calculate forces.
• Engineering: Fractions and proportions are used in engineering to design and optimize systems.

Conclusion

Q: What is a fraction?

A: A fraction is a way of representing a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). For example, the fraction $\frac{1}{2}$ represents one half of a whole.

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is often expressed as a fraction, where the ratio of two quantities is equal to the ratio of two other quantities. For example, the proportion $\frac{7}{21} = \frac{3}{9}$ states that the ratio of 7 to 21 is equal to the ratio of 3 to 9.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, to simplify the fraction $\frac{12}{18}$, you would find the GCD of 12 and 18, which is 6, and then divide both numbers by 6 to get the simplified fraction: $\frac{12}{18} = \frac{2}{3}$.

Q: What is the difference between a proper fraction and an improper fraction?

A: A proper fraction is a fraction where the numerator is less than the denominator. For example, the fraction $\frac{1}{2}$ is a proper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, the fraction $\frac{3}{2}$ is an improper fraction.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a proper fraction. For example, the mixed number $2\frac{1}{2}$ represents two and a half. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, the fraction $\frac{3}{2}$ is an improper fraction.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. Then, you need to write the result as a fraction with the denominator. For example, to convert the mixed number $2\frac{1}{2}$ to an improper fraction, you would multiply 2 by 2 and add 1 to get 5, and then write the result as the fraction $\frac{5}{2}$.

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator and write the result as a whole number and a remainder. Then, you need to write the remainder as a fraction with the denominator. For example, to convert the improper fraction $\frac{5}{2}$ to a mixed number, you would divide 5 by 2 to get 2 with a remainder of 1, and then write the result as the mixed number $2\frac{1}{2}$.

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

A: Equivalent fractions are fractions that have the same value. For example, the fractions $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions. Equivalent ratios are ratios that have the same value. For example, the ratios 2:4 and 1:2 are equivalent ratios.

Q: How do I find equivalent fractions?

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

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. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

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 greatest common factor. For example, to find the GCD of 12 and 18, you could list the factors of each number and find the greatest common factor, which is 6.

Conclusion

In conclusion, fractions and proportions are fundamental concepts in mathematics that have numerous real-world applications. By understanding fractions and proportions, you can solve problems more efficiently and effectively. We hope that this FAQ has helped you to better understand fractions and proportions and has answered any questions you may have had.