Simplifying the Answer Fully

Oct 13, 2025 by miodeya.com 130 views

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Introduction

Multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together. In this article, we will focus on simplifying the answer fully for the given problem: $\frac{7}{9} \cdot \frac{4}{5}$ .

What are Fractions?

A fraction is a way to represent a part of a whole. It consists of two numbers: a numerator and a denominator. The numerator represents the number of equal parts, and the denominator represents the total number of parts. For example, the fraction $\frac{1}{2}$ represents one half of a whole.

Multiplying Fractions

When multiplying fractions, we multiply the numerators together and the denominators together. This is represented by the following formula:

$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$

Simplifying the Answer Fully

Now, let's apply this formula to the given problem: $\frac{7}{9} \cdot \frac{4}{5}$ .

$\frac{7}{9} \cdot \frac{4}{5} = \frac{7 \cdot 4}{9 \cdot 5}$

Calculating the Numerator and Denominator

To simplify the answer fully, we need to calculate the numerator and denominator separately.

Numerator: $7 \cdot 4 = 28$

Denominator: $9 \cdot 5 = 45$

Writing the Answer in Simplest Form

Now that we have the numerator and denominator, we can write the answer in its simplest form.

$\frac{28}{45}$

Is the Answer in Its Simplest Form?

To determine if the answer is in its simplest form, we need to check if the numerator and denominator have any common factors. If they do, we can simplify the answer further.

Finding Common Factors

To find common factors, we can list the factors of the numerator and denominator.

Factors of 28: 1, 2, 4, 7, 14, 28

Factors of 45: 1, 3, 5, 9, 15, 45

Identifying Common Factors

From the list of factors, we can see that the common factors of 28 and 45 are 1.

Simplifying the Answer Further

Since the common factors are 1, we cannot simplify the answer further. The answer is already in its simplest form.

Conclusion

In conclusion, the answer to the problem $\frac{7}{9} \cdot \frac{4}{5}$ is $\frac{28}{45}$ . This answer is in its simplest form, and we cannot simplify it further.

Frequently Asked Questions

Q: What is the formula for multiplying fractions?

A: The formula for multiplying fractions is $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$ .

Q: How do I simplify the answer fully?

A: To simplify the answer fully, you need to calculate the numerator and denominator separately and then check if they have any common factors. If they do, you can simplify the answer further.

Q: What are common factors?

A: Common factors are the numbers that divide both the numerator and denominator without leaving a remainder.

Q: How do I find common factors?

A: To find common factors, you can list the factors of the numerator and denominator and then identify the common factors.

Final Answer

The final answer to the problem $\frac{7}{9} \cdot \frac{4}{5}$ is $\frac{28}{45}$ .

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Introduction

Multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together. In this article, we will focus on answering frequently asked questions related to multiplying fractions.

Q: What is the formula for multiplying fractions?

A: The formula for multiplying fractions is $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$ .

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to multiply the numerators together and the denominators together. For example, to multiply $\frac{1}{2}$ and $\frac{3}{4}$ , you would multiply the numerators together (1 and 3) and the denominators together (2 and 4).

Q: How do I simplify the answer fully?

A: To simplify the answer fully, you need to calculate the numerator and denominator separately and then check if they have any common factors. If they do, you can simplify the answer further.

Q: What are common factors?

A: Common factors are the numbers that divide both the numerator and denominator without leaving a remainder.

Q: How do I find common factors?

A: To find common factors, you can list the factors of the numerator and denominator and then identify the common factors.

Q: Can I simplify a fraction with a numerator and denominator that have no common factors?

A: Yes, you can simplify a fraction with a numerator and denominator that have no common factors. In this case, the fraction is already in its simplest form.

Q: How do I multiply fractions with negative numbers?

A: To multiply fractions with negative numbers, you need to multiply the numerators together and the denominators together, just like with positive numbers. However, if one or both of the fractions have a negative sign, you need to multiply the result by -1.

Q: Can I multiply a fraction by a whole number?

A: Yes, you can multiply a fraction by a whole number. To do this, you need to multiply the numerator by the whole number and keep the denominator the same.

Q: How do I multiply a fraction by a decimal?

A: To multiply a fraction by a decimal, you need to convert the decimal to a fraction and then multiply the fractions together.

Q: Can I multiply a fraction by a percentage?

A: Yes, you can multiply a fraction by a percentage. To do this, you need to convert the percentage to a decimal and then multiply the fraction by the decimal.

Q: How do I multiply fractions with variables?

A: To multiply fractions with variables, you need to multiply the numerators together and the denominators together, just like with numbers. However, you need to use the rules of algebra to simplify the result.

Q: Can I multiply a fraction by a mixed number?

A: Yes, you can multiply a fraction by a mixed number. To do this, you need to convert the mixed number to an improper fraction and then multiply the fractions together.

Q: How do I multiply fractions with different signs?

A: To multiply fractions with different signs, you need to multiply the numerators together and the denominators together, just like with numbers. However, if the signs are different, you need to multiply the result by -1.

Q: Can I multiply a fraction by a fraction with a zero denominator?

A: No, you cannot multiply a fraction by a fraction with a zero denominator. This is because division by zero is undefined.

Q: How do I multiply fractions with complex numbers?

A: To multiply fractions with complex numbers, you need to multiply the numerators together and the denominators together, just like with numbers. However, you need to use the rules of complex numbers to simplify the result.

Q: Can I multiply a fraction by a fraction with a negative exponent?

A: Yes, you can multiply a fraction by a fraction with a negative exponent. To do this, you need to multiply the numerators together and the denominators together, just like with numbers. However, you need to use the rules of exponents to simplify the result.

Q: How do I multiply fractions with different bases?

A: To multiply fractions with different bases, you need to multiply the numerators together and the denominators together, just like with numbers. However, you need to use the rules of exponents to simplify the result.

Q: Can I multiply a fraction by a fraction with a variable exponent?

A: Yes, you can multiply a fraction by a fraction with a variable exponent. To do this, you need to multiply the numerators together and the denominators together, just like with numbers. However, you need to use the rules of exponents to simplify the result.

Q: How do I multiply fractions with different units?

A: To multiply fractions with different units, you need to convert the units to a common unit and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a unit that is not a multiple of the other unit?

A: No, you cannot multiply a fraction by a fraction with a unit that is not a multiple of the other unit. This is because the units must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different scales?

A: To multiply fractions with different scales, you need to convert the scales to a common scale and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a scale that is not a multiple of the other scale?

A: No, you cannot multiply a fraction by a fraction with a scale that is not a multiple of the other scale. This is because the scales must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different units of measurement?

A: To multiply fractions with different units of measurement, you need to convert the units of measurement to a common unit of measurement and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a unit of measurement that is not a multiple of the other unit of measurement?

A: No, you cannot multiply a fraction by a fraction with a unit of measurement that is not a multiple of the other unit of measurement. This is because the units of measurement must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different time units?

A: To multiply fractions with different time units, you need to convert the time units to a common time unit and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a time unit that is not a multiple of the other time unit?

A: No, you cannot multiply a fraction by a fraction with a time unit that is not a multiple of the other time unit. This is because the time units must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different spatial units?

A: To multiply fractions with different spatial units, you need to convert the spatial units to a common spatial unit and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a spatial unit that is not a multiple of the other spatial unit?

A: No, you cannot multiply a fraction by a fraction with a spatial unit that is not a multiple of the other spatial unit. This is because the spatial units must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different quantities?

A: To multiply fractions with different quantities, you need to convert the quantities to a common quantity and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a quantity that is not a multiple of the other quantity?

A: No, you cannot multiply a fraction by a fraction with a quantity that is not a multiple of the other quantity. This is because the quantities must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different rates?

A: To multiply fractions with different rates, you need to convert the rates to a common rate and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a rate that is not a multiple of the other rate?

A: No, you cannot multiply a fraction by a fraction with a rate that is not a multiple of the other rate. This is because the rates must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different ratios?

A: To multiply fractions with different ratios, you need to convert the ratios to a common ratio and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a ratio that is not a multiple of the other ratio?

A: No, you cannot multiply a fraction by a fraction with a ratio that is not a multiple of the other ratio. This is because the ratios must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different proportions?

A: To multiply fractions with different proportions, you need to convert the proportions to a common proportion and then multiply the fractions together.

Q: Can I multiply a fraction by a fraction with a proportion that is not a multiple of the other proportion?

A: No, you cannot multiply a fraction by a fraction with a proportion that is not a multiple of the other proportion. This is because the proportions must be compatible in order to multiply the fractions.

Q: How do I multiply fractions with different scales of measurement?

A: To multiply