Problem 363 Multiply. $$ \left(-\frac{14... [FREE SOLUTION]

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Chapter 1: Problem 363

Multiply. $$ \left(-\frac{14}{15}\right)\left(\frac{9}{20}\right) $$

Short Answer

Expert verified

-\frac{21}{50}

Step by step solution

Understand the problem

The task requires us to multiply two fractions: $-\frac{14}{15}$ and $\frac{9}{20}$.

Multiply the numerators

Multiply the numerators of the two fractions:\[-14 \times 9 = -126\]

Multiply the denominators

Multiply the denominators of the two fractions:\[15 \times 20 = 300\]

Form the new fraction

Combine the results of the multiplication to form a new fraction:\[-\frac{126}{300}\]

Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 126 and 300 is 6:\[-\frac{126 \div 6}{300 \div 6} = -\frac{21}{50}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fraction Multiplication

When you multiply fractions, the process is straightforward. Start with the numerators. Multiply them to get the new numerator. Next, multiply the denominators to get the new denominator. For example, in the problem $-\frac{14}{15}$ and $\frac{9}{20}$, multiply -14 by 9 to get -126. Then, multiply 15 by 20 to get 300. The resulting fraction becomes $-\frac{126}{300}$.

Always make sure you multiply straight across.
Keep the sign of the fractions in mind.
Result will also be a fraction.

With fraction multiplication, there is no need to find a common denominator, as required in addition or subtraction.

Simplifying Fractions

Simplifying fractions is an essential skill. Once you have a fraction, you should reduce it to its lowest terms. This means dividing the numerator and the denominator by their greatest common divisor (GCD). In our example, the product is $-\frac{126}{300}$. To simplify it, find the GCD of 126 and 300.

Look for the largest number that divides both the numerator and denominator.
Use prime factorization if necessary.
If you can no longer divide both by the same number, it's simplified.

Here, dividing both 126 and 300 by their GCD, which is 6, we get $-\frac{21}{50}$.

Greatest Common Divisor

The greatest common divisor (GCD) is the largest number that evenly divides two or more numbers. It's crucial for simplifying fractions. To find the GCD:

List the factors of both the numerator and the denominator.
Identify the common factors.
Choose the largest common factor.

For $126$ and $300$, the GCD is $6$. This is because:
\126 = 2 \times 3^2 \times 7\
\300 = 2^2 \times 3 \times 5 \times 5\

The common factors are 2 and 3, and the highest factor is 6. So, you can simplify $-\frac{126}{300}$ to $-\frac{21}{50}$.

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91影视

Multiply. $$ \left(-\frac{14}{15}\right)\left(\frac{9}{20}\right) $$

Short Answer

Step by step solution

Understand the problem

Multiply the numerators

Multiply the denominators

Form the new fraction

Simplify the fraction

Key Concepts

Fraction Multiplication

Simplifying Fractions

Greatest Common Divisor

One App. One Place for Learning.

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