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Chapter 1: Problem 112

In the following exercises, simplify using the order of operations. $$ 4 \cdot 7+3 \cdot 5 $$

Short Answer

Expert verified
43

Step by step solution

01

- Apply multiplication

Perform the multiplications first as per the order of operations. Multiply 4 by 7 and 3 by 5. The expression becomes: \[4 \times 7 + 3 \times 5\] Calculate \[4 \times 7\] to get 28. Calculate \[3 \times 5\] to get 15.Now, the expression is: \[28 + 15\]
02

- Apply addition

Add the results from the previous multiplications. \[28 + 15 = 43\]

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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 basic arithmetic operations. It's the process of combining equal groups. In the context of the provided exercise, you must first perform the multiplication before any addition, due to the order of operations rule.

For example: In the expression\(4 \times 7 + 3 \times 5\), identify the multiplication components: \(4 \times 7\) and \(3 \times 5\).

You perform these calculations as follows:
  • Calculate \(4 \times 7\) to get 28.
  • Calculate \(3 \times 5\) to get 15.
It's essential to do these multiplications first before moving on to addition, adhering to the order of operations.
Addition
Addition is another fundamental arithmetic operation. It involves combining numbers to get their total. After you complete the multiplication steps in the exercise, you then proceed with addition.

Using the simplified components from the previous step: \(28 + 15\), you need to add these two numbers.

To do this:
  • Start with the number 28.
  • Add 15 to it.
The sum of 28 and 15 is 43. This demonstrates how following the correct order of operations allows you to accurately simplify expressions.
Simplifying Expressions
Simplifying expressions means reducing them to their simplest form by following the order of operations. This includes handling multiplication and addition correctly and in the right sequence.

For the exercise given: \(4 \times 7 + 3 \times 5\), the process begins with multiplication first, as explained earlier.

Once the multiplication of 4 by 7 and 3 by 5 is done, you simplify the expression to: \(28 + 15\).

Following this, the addition part comes into play, where adding 28 and 15 results in the final simplified form: 43.

Make sure to always handle each part of the expression step-by-step, performing multiplications before additions, to simplify correctly.

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