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Chapter 1: Problem 59

Find each product or quotient. $$ 9\left(\frac{2 y}{9}\right) $$

Short Answer

Expert verified
2y

Step by step solution

01

Understand the expression

The given expression is a product operation: \[ 9 \left( \frac{2y}{9} \right) \] Here, we are multiplying 9 by the fraction \( \frac{2y}{9} \).
02

Simplify the fraction

Notice that 9 is both the numerator and the denominator. This means they can be simplified because \[ 9 \div 9 = 1 \] So, the expression simplifies to: \[ 1 \left(2y\right) \]
03

Multiply by the remaining term

Now multiply 1 by the remaining term: \[ 1 \times 2y = 2y \]

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Key Concepts

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

Simplification
In algebra, simplification involves combining like terms and reducing expressions to their simplest form.
This makes calculations easier and solutions clearer.
In the given exercise, we have to simplify the expression \ \[ 9 \left( \frac{2y}{9} \right) \ \].
To do that, we look at both the numerator and the denominator.
Notice that 9 is both in the numerator and the denominator.
They cancel each other out because 9 divided by 9 equals 1.
This process is known as simplifying the fraction, which we'll cover next.
Fraction Multiplication
Fraction multiplication can be easier than it looks.
Here's how it works: multiply the numerators together and the denominators together.
But sometimes, it gets even simpler if common factors exist in the numerator and denominator.
In our example, \ \[ 9 \left( \frac{2y}{9} \right) \ \], the 9s cancel each other out.
Thus, the fraction \ \[ \frac{9}{9} \ \] simplifies to 1.
So, you're left with \ \[ 1 \times 2y \].
When you multiply 1 by any number, the result is the same number.
Therefore, the result is 2y.
Basic Algebra
Basic algebra is the foundation of many mathematical concepts and involves operations with variables and constants.
In our case, the variable is y, and we are performing basic operations like multiplication.
Understanding how to handle expressions like \ \[ 9 \left( \frac{2y}{9} \ \] makes solving more complex algebraic problems easier in the future.
The goal is to simplify and solve for the variable or understand the expression better.
Always start by simplifying the parts of the expression and gradually solve step-by-step.

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Most popular questions from this chapter

Simplify each expression. $$ 5\left(x^{2}-6 x+4\right)+4\left(x^{2}+3 x-1\right) $$

Simplify each expression. $$ 0.1(x+5)-0.04(x+50) $$

Write an algebraic expression for each problem. Parallelogram. The lengths of the sides of a lot in the shape of a parallelogram are \(w\) feet and \(w+50\) feet. What is its perimeter? Is it possible to find the area from this information?

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Solve each problem. Perimeter of a pool. The algebraic expression \(2 L+2 W\) gives the perimeter of a rectangle with length \(L\) and width \(W\). Find the perimeter of a rectangular swimming pool that has length 34 feet and width 18 feet.
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