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Chapter 4: Problem 56

Simplify. $$ (26.2-14.8) \times 12 $$

Short Answer

Expert verified
136.8

Step by step solution

01

- Perform the Subtraction Inside the Parentheses

First, calculate the difference inside the parentheses: \(26.2 - 14.8 = 11.4\)
02

- Multiply the Result by 12

Next, take the result from Step 1 and multiply it by 12: \(11.4 \times 12 = 136.8\)

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Key Concepts

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

Subtraction
In arithmetic, subtraction is the process of taking one number away from another. It is denoted by the minus sign (鈭�). To perform a subtraction:
  • Identify the minuend (the number you start with)
  • Identify the subtrahend (the number you subtract)
  • Subtract the subtrahend from the minuend
For example, in the given exercise:
\(26.2 - 14.8\) Here, 26.2 is the minuend, and 14.8 is the subtrahend. When we subtract 14.8 from 26.2, we get 11.4. Remember to align the decimal points correctly for accurate results.
Multiplication
Multiplication involves calculating the product of two numbers. It is indicated by the multiplication sign (脳). To perform multiplication:
  • Write the numbers one below the other
  • Multiply each digit of the top number by each digit of the bottom number, moving from right to left
  • Add the results, considering the position of the digits (place value)
In the exercise: \(11.4 \times 12\) First, multiply 11.4 by 12. Multiplying decimals follows the same rules as whole numbers, but it's important to place the decimal point correctly in the product. The placement is found by counting the total number of decimal places in the numbers being multiplied.
Order of Operations
The order of operations is crucial in mathematics to determine the sequence of steps to solve an expression correctly. The rules are often remembered by the acronym PEMDAS:
  • Parentheses first
  • Exponents (ie Powers and Square Roots, etc.)
  • Multiplication and Division (left-to-right)
  • Addition and Subtraction (left-to-right)

In the exercise: \((26.2 - 14.8) \times 12\) We start with the parentheses, so first do the subtraction: \(26.2 - 14.8 = 11.4\). Next, we handle the multiplication: \(11.4 \times 12 = 136.8\). Following the order of operations ensures we simplify expressions accurately.

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