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Chapter 1: Problem 27

Simplify each numerical expression. (Objective 2) $$4 \cdot 9 \div 12+18 \div 2+3$$

Short Answer

Expert verified
The simplified expression is 15.

Step by step solution

01

Perform Multiplication

The expression is \(4 \cdot 9 \div 12 + 18 \div 2 + 3\). According to the order of operations (PEMDAS/BODMAS), start with multiplication: \(4 \cdot 9 = 36\). The expression now is \(36 \div 12 + 18 \div 2 + 3\).
02

Perform First Division

Next, perform the division from left to right. Divide 36 by 12: \(36 \div 12 = 3\). The expression becomes \(3 + 18 \div 2 + 3\).
03

Perform Second Division

Continue with the second division: 18 divided by 2. \(18 \div 2 = 9\). The expression now is \(3 + 9 + 3\).
04

Perform Addition

Finally, add the remaining numbers together. First, \(3 + 9 = 12\), then add 3: \(12 + 3 = 15\). Therefore, the simplified expression is 15.

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Key Concepts

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

Understanding Multiplication
Multiplication is an arithmetic operation that combines groups of equal sizes. Think of it as repeated addition. In mathematics, when we see something like \(4 \cdot 9\), we are essentially adding four sets of nine together: \(9 + 9 + 9 + 9\).
  • In our example, the task \(4 \cdot 9\) equals 36. This tells us that adding up four lots of nine will give us a total of 36.
  • When dealing with expressions, it's important to perform multiplication before moving to other operations like addition and subtraction, following the order of operations.
The memory aid PEMDAS (or BODMAS) can help remember the sequence: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Addressing multiplication first helps eliminate potential calculation errors later.
Understanding Division
Division is like sharing or grouping. When you divide, you're essentially seeing how many times a number can fit into another. For instance, dividing 36 by 12 in our example implies finding out how many sets of 12 fit into 36.
  • By dividing 36 by 12, we get 3. It means three groups of 12 make up 36.
  • In expressions, division should be handled after multiplication if both operations are present, but before addition and subtraction.
Remember, as with multiplication, you should tackle division from left to right, in sequence with any other multiplication operations in your equation.
Teaching yourself this skill ensures expressions are simplified correctly and consistently.
Understanding Addition
Addition involves bringing two or more numbers together to create a total or sum. It's one of the most basic arithmetic operations and comes towards the end of our operations sequence when simplifying expressions.
  • In our example, we start with \(3 + 9\) which sums up to 12. Then, adding the remaining 3 gives us 15.
  • As part of the order of operations, tackle addition last to ensure any multiplication and division are resolved first. This hierarchy avoids making errors in the final sum.
Mastering addition in the context of multiple operations helps in efficiently handling more complex mathematical expressions and problems.
Being comfortable with these steps makes calculations straightforward and error-free.

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Most popular questions from this chapter

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