Multiplying the Fraction by the Reciprocal of 9

Oct 13, 2025 by leolavanderia.com.br 11 views

Introduction

When it comes to evaluating mathematical expressions, there are several operations that we need to perform in a specific order. In this article, we will focus on evaluating the expression $\frac{3}{5} \div 9$ . This expression involves division, which is one of the four basic arithmetic operations. To evaluate this expression, we need to understand the concept of division and how it is performed.

Understanding Division

Division is the process of finding the quotient of two numbers. It is the inverse operation of multiplication. When we divide a number by another number, we are essentially finding how many times the second number fits into the first number. For example, if we divide 12 by 3, we get 4, because 3 fits into 12 four times.

Evaluating the Expression

To evaluate the expression $\frac{3}{5} \div 9$ , we need to follow the order of operations (PEMDAS). The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

In this expression, we have a fraction $\frac{3}{5}$ and a number 9. We need to divide the fraction by 9. To do this, we can multiply the fraction by the reciprocal of 9, which is $\frac{1}{9}$ . This is because division is the inverse operation of multiplication.

Multiplying the Fraction by the Reciprocal of 9

To multiply the fraction $\frac{3}{5}$ by the reciprocal of 9, we can multiply the numerators and denominators separately. The numerator of the fraction is 3, and the denominator is 5. The reciprocal of 9 is $\frac{1}{9}$ . So, we can multiply the numerators and denominators as follows:

$\frac{3}{5} \times \frac{1}{9} = \frac{3 \times 1}{5 \times 9}$

Simplifying the Expression

Now that we have multiplied the fraction by the reciprocal of 9, we can simplify the expression. To simplify the expression, we can cancel out any common factors between the numerator and denominator. In this case, there are no common factors between 3 and 9, but there is a common factor between 5 and 9, which is 5.

So, we can cancel out the common factor of 5 as follows:

$\frac{3 \times 1}{5 \times 9} = \frac{3}{5 \times 3}$

Final Answer

Now that we have simplified the expression, we can find the final answer. To find the final answer, we can divide the numerator by the denominator. In this case, the numerator is 3, and the denominator is 15.

So, the final answer is:

$\frac{3}{15} = \frac{1}{5}$

Conclusion

In this article, we evaluated the expression $\frac{3}{5} \div 9$ . We used the concept of division and the order of operations (PEMDAS) to evaluate the expression. We also multiplied the fraction by the reciprocal of 9 and simplified the expression to find the final answer. The final answer is $\frac{1}{5}$ .

Frequently Asked Questions

What is the order of operations (PEMDAS)? The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
What is the concept of division? Division is the process of finding the quotient of two numbers. It is the inverse operation of multiplication.
How do we multiply a fraction by the reciprocal of a number? To multiply a fraction by the reciprocal of a number, we can multiply the numerators and denominators separately.
How do we simplify an expression? To simplify an expression, we can cancel out any common factors between the numerator and denominator.

References

[1] Khan Academy. (n.d.). Division. Retrieved from <https://www.khanacademy.org/math/algebra/x2f6b7d7d-x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d7d/x2f6b7d

Q: What is the order of operations (PEMDAS)?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: What is the concept of division?

A: Division is the process of finding the quotient of two numbers. It is the inverse operation of multiplication.

Q: How do we multiply a fraction by the reciprocal of a number?

A: To multiply a fraction by the reciprocal of a number, we can multiply the numerators and denominators separately.

Q: How do we simplify an expression?

A: To simplify an expression, we can cancel out any common factors between the numerator and denominator.

Q: What is the final answer to the expression $\frac{3}{5} \div 9$ ?

A: The final answer to the expression $\frac{3}{5} \div 9$ is $\frac{1}{5}$ .

Q: Can we use a calculator to evaluate the expression $\frac{3}{5} \div 9$ ?

A: Yes, we can use a calculator to evaluate the expression $\frac{3}{5} \div 9$ . However, it's always a good idea to understand the concept behind the calculation.

Q: How do we handle fractions in division?

A: When dividing a fraction by a number, we can multiply the fraction by the reciprocal of the number.

Q: Can we divide a fraction by another fraction?

A: Yes, we can divide a fraction by another fraction. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle negative numbers in division?

A: When dividing a negative number by another number, we can multiply the negative number by the reciprocal of the other number.

Q: Can we divide a decimal by a fraction?

A: Yes, we can divide a decimal by a fraction. To do this, we can convert the decimal to a fraction and then divide the fraction by the other fraction.

Q: How do we handle mixed numbers in division?

A: When dividing a mixed number by another number, we can convert the mixed number to an improper fraction and then divide the fraction by the other number.

Q: Can we divide a fraction by a decimal?

A: Yes, we can divide a fraction by a decimal. To do this, we can convert the decimal to a fraction and then divide the fraction by the other fraction.

Q: How do we handle complex fractions in division?

A: When dividing a complex fraction by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a negative number?

A: Yes, we can divide a fraction by a negative number. To do this, we can multiply the fraction by the reciprocal of the negative number.

Q: How do we handle fractions with variables in division?

A: When dividing a fraction with a variable by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a variable?

A: Yes, we can divide a fraction by a fraction with a variable. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with exponents in division?

A: When dividing a fraction with an exponent by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with an exponent?

A: Yes, we can divide a fraction by a fraction with an exponent. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with radicals in division?

A: When dividing a fraction with a radical by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a radical?

A: Yes, we can divide a fraction by a fraction with a radical. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with absolute values in division?

A: When dividing a fraction with an absolute value by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with an absolute value?

A: Yes, we can divide a fraction by a fraction with an absolute value. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with inequalities in division?

A: When dividing a fraction with an inequality by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with an inequality?

A: Yes, we can divide a fraction by a fraction with an inequality. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with functions in division?

A: When dividing a fraction with a function by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a function?

A: Yes, we can divide a fraction by a fraction with a function. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with matrices in division?

A: When dividing a fraction with a matrix by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a matrix?

A: Yes, we can divide a fraction by a fraction with a matrix. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with determinants in division?

A: When dividing a fraction with a determinant by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a determinant?

A: Yes, we can divide a fraction by a fraction with a determinant. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with eigenvalues in division?

A: When dividing a fraction with an eigenvalue by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with an eigenvalue?

A: Yes, we can divide a fraction by a fraction with an eigenvalue. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with eigenvectors in division?

A: When dividing a fraction with an eigenvector by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with an eigenvector?

A: Yes, we can divide a fraction by a fraction with an eigenvector. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with singular matrices in division?

A: When dividing a fraction with a singular matrix by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a singular matrix?

A: Yes, we can divide a fraction by a fraction with a singular matrix. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with non-singular matrices in division?

A: When dividing a fraction with a non-singular matrix by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a non-singular matrix?

A: Yes, we can divide a fraction by a fraction with a non-singular matrix. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with orthogonal matrices in division?

A: When dividing a fraction with an orthogonal matrix by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with an orthogonal matrix?

A: Yes, we can divide a fraction by a fraction with an orthogonal matrix. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with unitary matrices in division?

A: When dividing a fraction with a unitary matrix by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a unitary matrix?

A: Yes, we can divide a fraction by a fraction with a unitary matrix. To do this, we can multiply the first fraction by the reciprocal of the second fraction.

Q: How do we handle fractions with Hermitian matrices in division?

A: When dividing a fraction with a Hermitian matrix by another fraction, we can multiply the first fraction by the reciprocal of the second fraction.

Q: Can we divide a fraction by a fraction with a Hermitian matrix?

A: Yes, we can divide a fraction by a fraction with a Hermitian matrix. To do this, we can multiply the first fraction by the reciprocal of the second fraction.