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Chapter 1: Problem 744

Simplify. $$ 20\left(\frac{3}{5} q\right) $$

Short Answer

Expert verified
12q

Step by step solution

01

- Distribute the 20

Multiply 20 with the fraction \ \( \frac{3}{5} \). This means calculating \ \( 20 \times \frac{3}{5} \).
02

- Simplify the Multiplication

Perform the multiplication: \ \( 20 \times \frac{3}{5} = \frac{20 \times 3}{5} = \frac{60}{5} \).
03

- Simplify the Fraction

Simplify the fraction: \ \( \frac{60}{5} = 12 \).
04

- Combine with the Variable

Combine the simplified result with the variable \ \( q \): \ \( 12q \).

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Key Concepts

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

Distributive Property
The distributive property allows us to multiply a single term by each term inside a set of parentheses. In this exercise, we need to multiply 20 by the fraction \(\frac{3}{5} q\).

If you see an expression like 20(\(\frac{3}{5} q\)), it means you should distribute, or multiply, the 20 by \(\frac{3}{5} q\). This step is crucial for simplifying expressions and solving equations.

To distribute correctly:
  • Multiply the number outside the parentheses by the numerator of the fraction.
  • Keep the denominator as it is.
  • Finally, multiply the result by the variable, if there's one.


In this exercise:
  • 20 is multiplied by \(\frac{3}{5}\).
  • The variable \( q \) remains consistent throughout the operation.
Multiplication of Fractions
Multiplying fractions involves multiplying the numerators together and the denominators together.

For instance, given the multiplication step here, \(\frac{3}{5} \times 20\), you can think of 20 as \(\frac{20}{1}\). This makes the multiplication straightforward:

  • Multiply the numerators: \(\frac{3 \times 20}{5 \times 1}\) = \(\frac{60}{5}\).


After this step, the exercise becomes easier, as evidenced by it transforming into a simple fraction that we can now simplify. Multiplying by fractions is an essential skill because it keeps our equations manageable and understandable.
Simplifying Fractions
Simplifying fractions means reducing them to their lowest terms. For the fraction \(\frac{60}{5}\):

  • Divide the numerator by the denominator: \(\frac{60}{5} = 12\)


This reduction makes the expression simpler and easier to understand.

Simplifying is a critical concept in algebra and helps in verifying the correctness of your solution.

Once simplified, you attach the variable (if any), giving the final simplified expression, \( 12q \).

Always check your fractions to see if they can be simplified鈥攊t keeps your math clean and manageable.

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Most popular questions from this chapter

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