Multiply: \left(-\frac{5}{11}\right)\left(\frac{-1}{-3}\right)\left(\frac{33}{35}\right ] ( − 5 11 ) ( − 1 − 3 ) ( 33 35 ) = □ \left(-\frac{5}{11}\right)\left(\frac{-1}{-3}\right)\left(\frac{33}{35}\right) = \square ( − 11 5 ) ( − 3 − 1 ) ( 35 33 ) = □ (Type An Integer, Proper Fraction, Or Mixed Number.

Mar 10, 2025 by ADMIN 311 views

$Multiply: $\left(-\frac{5}{11}\right)\left(\frac{-1}{-3}\right)\left(\frac{33}{35}\right)$$

Introduction

When it comes to multiplying fractions, it's essential to understand the rules and procedures involved. In this article, we will delve into the world of fraction multiplication, exploring the concept of multiplying fractions with negative numbers and simplifying the resulting expression.

Understanding Fraction Multiplication

To multiply fractions, we need to multiply the numerators together and the denominators together. This is a fundamental rule in mathematics, and it applies to all types of fractions, including those with negative numbers.

Multiplying Fractions with Negative Numbers

When multiplying fractions with negative numbers, we need to remember that a negative number multiplied by another negative number results in a positive number. This is a crucial concept to grasp, as it will help us simplify the expression and arrive at the correct answer.

The Problem

The problem we are given is to multiply the following fractions:

$\left(-\frac{5}{11}\right)\left(\frac{-1}{-3}\right)\left(\frac{33}{35}\right)$

Step 1: Multiply the Numerators

To start, we need to multiply the numerators together. The numerators are -5, -1, and 33. When we multiply these numbers together, we get:

$-5 \times -1 \times 33 = 165$

Step 2: Multiply the Denominators

Next, we need to multiply the denominators together. The denominators are 11, -3, and 35. When we multiply these numbers together, we get:

$11 \times -3 \times 35 = -1155$

Step 3: Simplify the Expression

Now that we have multiplied the numerators and denominators together, we can simplify the expression. We can start by simplifying the numerator and denominator separately.

Simplifying the Numerator

The numerator is 165. We can simplify this number by dividing it by its greatest common divisor (GCD). The GCD of 165 is 15, so we can divide 165 by 15 to get:

$\frac{165}{15} = 11$

Simplifying the Denominator

The denominator is -1155. We can simplify this number by dividing it by its greatest common divisor (GCD). The GCD of -1155 is 15, so we can divide -1155 by 15 to get:

$\frac{-1155}{15} = -77$

Step 4: Write the Final Answer

Now that we have simplified the expression, we can write the final answer. The final answer is:

$\frac{11}{-77}$

Conclusion

In this article, we have explored the concept of multiplying fractions with negative numbers and simplifying the resulting expression. We have applied the rules of fraction multiplication and simplified the expression to arrive at the final answer. The final answer is $\frac{11}{-77}$ .

Final Answer

The final answer is $\boxed{-\frac{11}{77}}$ .

Introduction

In our previous article, we explored the concept of multiplying fractions with negative numbers and simplifying the resulting expression. We applied the rules of fraction multiplication and arrived at the final answer. In this article, we will continue to provide more information and answer frequently asked questions related to the topic.

Q&A

Q: What is the rule for multiplying fractions with negative numbers?

A: When multiplying fractions with negative numbers, we need to remember that a negative number multiplied by another negative number results in a positive number.

Q: How do I simplify a fraction after multiplying it with another fraction?

A: To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. We can then divide both the numerator and denominator by the GCD to simplify the fraction.

Q: What is the difference between multiplying fractions and adding fractions?

A: Multiplying fractions involves multiplying the numerators together and the denominators together, whereas adding fractions involves finding a common denominator and adding the numerators together.

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 simply multiply the numerator of the fraction by the whole number.

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

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

Q: What is the order of operations when multiplying fractions?

A: The order of operations when multiplying fractions is:

Multiply the numerators together
Multiply the denominators together
Simplify the resulting fraction

Q: Can I multiply a negative fraction by a positive fraction?

A: Yes, you can multiply a negative fraction by a positive fraction. The result will be a negative fraction.

Q: How do I multiply a fraction by a fraction with a negative exponent?

A: To multiply a fraction by a fraction with a negative exponent, you can rewrite the fraction with a positive exponent and then multiply the fractions together.

Q: What is the difference between multiplying fractions and dividing fractions?

A: Multiplying fractions involves multiplying the numerators together and the denominators together, whereas dividing fractions involves inverting the second fraction and multiplying the fractions together.

Conclusion

In this article, we have provided answers to frequently asked questions related to multiplying fractions with negative numbers and simplifying the resulting expression. We have also covered other topics related to fraction multiplication, including simplifying fractions, multiplying fractions by whole numbers and decimals, and the order of operations when multiplying fractions.

Final Answer

The final answer is $\boxed{-\frac{11}{77}}$ .