Problem 62 Simplify. $$ 123.3-4.24 \tim... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 4: Problem 62

Simplify. $$ 123.3-4.24 \times 1.01 $$

Short Answer

Expert verified

The simplified result is 119.0176.

Step by step solution

- Understand the order of operations

Remember that the order of operations (PEMDAS/BODMAS) dictates that multiplication should be performed before subtraction.

- Perform the multiplication

Calculate the result of the multiplication: \[ 4.24 \times 1.01 \ = 4.24 \times (1 + 0.01) \- \text{using distributive property}- \ = 4.24 \times 1 + 4.24 \times 0.01 \- \ = 4.24 + 0.0424 = 4.2824 \]

- Perform the subtraction

Now subtract the result from 123.3: \[ 123.3 - 4.2824 = 119.0176 \]

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Key Concepts

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

Multiplication

Multiplication is one of the fundamental arithmetic operations. When you multiply two numbers, you repeatedly add one of the numbers to itself based on the value of the other number. For example, to multiply 4.24 and 1.01, you can think of it as:

Multiplying 4.24 by 1, which equals 4.24
Multiplying 4.24 by 0.01, which equals 0.0424

Combining these results, we get 4.24 + 0.0424, which equals 4.2824. Understanding how multiplication breaks down helps in more complex problems. Always follow the correct order of operations when dealing with more than one arithmetic operation.

Subtraction

Subtraction is another basic arithmetic operation where we take away one quantity from another. In the context of our exercise, after calculating the product from the multiplication step, we subtract this result from 123.3. The subtraction operation is straightforward:

The result from multiplication is 4.2824
Now subtract that from 123.3: 123.3 - 4.2824

This gives us 119.0176. Note that subtracting numbers with more decimal places might require attention to detail, making sure each digit is correctly aligned.

Distributive Property

The distributive property is a useful algebraic property that helps simplify expressions. It states that for any numbers a, b, and c:

$a \times (b + c) = (a \times b) + (a \times c)$

We used the distributive property to simplify our multiplication:

$4.24 \times 1.01$
This can be written as $4.24 \times (1 + 0.01)$
Which further simplifies to $ (4.24 \times 1) + (4.24 \times 0.01)$
And then to $4.24 + 0.0424$

Breaking down multiplication using the distributive property, as shown, simplifies the process and helps verify accuracy. Remember, proper usage of the distributive property can make complex multiplications more manageable.

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91影视

Simplify. $$ 123.3-4.24 \times 1.01 $$

Short Answer

Step by step solution

- Understand the order of operations

- Perform the multiplication

- Perform the subtraction

Key Concepts

Multiplication

Subtraction

Distributive Property

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