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Chapter 5: Problem 249

Simplify. \(\frac{5}{12}(30.58+17.9)\)

Short Answer

Expert verified
20.2

Step by step solution

01

- Add the numbers inside the parentheses

First, perform the addition inside the parentheses. Add 30.58 and 17.9 together. 30.58 + 17.9 = 48.48
02

- Multiply the fraction by the sum

Next, multiply the fraction \(\frac{5}{12}\) by the sum obtained in Step 1 (48.48). \(\frac{5}{12} \times 48.48\)
03

- Perform the multiplication

To multiply the fraction by the sum, multiply 48.48 by the numerator and then divide by the denominator. \(\frac{5 \times 48.48}{12} = \frac{242.4}{12} = 20.2\)

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Key Concepts

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

Simplifying Fractions
Fractions can sometimes look very complex, but simplifying them can make operations much easier. Simplifying a fraction means reducing it to its smallest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). For instance, the fraction \(\frac{30}{36}\) can be simplified. Both 30 and 36 can be divided by 6 (their GCD), resulting in \(\frac{5}{6}\). This simple form is easier to work with in any mathematical problem.
Order of Operations
In mathematics, it's crucial to follow a specific sequence when performing calculations. This sequence is known as the order of operations. The widely accepted acronym to help remember this order is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). For instance, in the problem \( \frac{5}{12}(30.58+17.9) \), you first solve the expression inside the parentheses before moving on to any multiplication. This ensures your answer is accurate.
Basic Arithmetic
Basic arithmetic involves fundamental operations such as addition, subtraction, multiplication, and division. These are foundational skills necessary for all areas of mathematics. For example, in the step where we add 30.58 and 17.9, we are using basic addition to combine the two numbers inside the parentheses:
30.58 + 17.9 = 48.48. These arithmetic operations are regularly used in more complex problems, so it's important to feel comfortable with them.
Prealgebra Steps
Prealgebra serves as the bridge between basic arithmetic and more advanced algebra concepts. It deals with fundamental steps that help to solve algebraic expressions systematically. When you encounter a problem such as \( \frac{5}{12} \times 48.48 \), breaking it down into clear steps is crucial:
  • First, you multiply the numerator 5 by 48.48 to get 242.4.

  • Next, you divide this product by the denominator 12 to get the simplified result of 20.2.

This systematic approach ensures accuracy and gradually builds up your mathematical skills.

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