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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

01

- Understand the order of operations

Remember that the order of operations (PEMDAS/BODMAS) dictates that multiplication should be performed before subtraction.
02

- Perform the multiplication

Calculate the result of the multiplication: \[ 4.24 \times 1.01 \ = 4.24 \times (1 + 0.01) \- \text{using distributive property}- \ = 4.24 \times 1 + 4.24 \times 0.01 \- \ = 4.24 + 0.0424 = 4.2824 \]
03

- 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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Most popular questions from this chapter

In order to make money on loans, financial institutions must be paid back more money than they loan. Suppose you borrow \(\$ 120,000\) to buy a house and agree to make monthly payments of \(\$ 872.67\) for 15 years. How much do you pay back altogether? How much more do you pay back than the amount of the loan?

Add. $$ 39+1.007 $$

What is the cost of 12.6 gal of gasoline at \(\$ 2.89\) per gallon? Round the answer to the nearest cent.

Peggy filled her van's gas tank and noted that the odometer read 26,342.8 . After the next fill-up, the odometer read 26,736.7 . It took 19.5 gal to fill the tank. How many miles per gallon did the van get between fill-ups?

Add. $$ \begin{array}{r} 9.104 \\ +123.456 \\ \hline \end{array} $$
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