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Chapter 1: Problem 63

Evaluate the given expression. Remember to follow the order of operations. $$15-5 \cdot 3$$

Short Answer

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Step by step solution

01

- Identify the operations involved

The expression given is $$15 - 5 \times 3$$. The operations involved are subtraction and multiplication.
02

- Apply the order of operations (PEMDAS/BODMAS)

According to the order of operations (PEMDAS/BODMAS), multiplication and division are performed before addition and subtraction. Identify the multiplication operation in the expression: $$5 \times 3$$.
03

- Perform the multiplication

Calculate the result of the multiplication: $$5 \times 3 = 15$$
04

- Substitute the result back into the expression

Replace the multiplication operation in the original expression with the result: $$15 - 15$$
05

- Perform the subtraction

Subtract the numbers: $$15 - 15 = 0$$

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Key Concepts

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

PEMDAS
When solving mathematical expressions, it's crucial to perform operations in a specific order. This order can be remembered using the acronym PEMDAS, which stands for:
  • P - Parentheses
  • E - Exponents
  • M - Multiplication
  • D - Division
  • A - Addition
  • S - Subtraction

PEMDAS helps ensure that everyone solves the same expression the same way and gets the same result. Keep in mind that multiplication and division are performed from left to right, as they appear in the expression. The same rule applies to addition and subtraction. In our example, we first handle the multiplication before the subtraction.
Subtraction
Subtraction is one of the basic arithmetic operations, symbolized by the minus sign (-). In its simplest terms, it means taking one number away from another. When performing subtraction:
  • Identify the numbers involved. For example, in the expression 15 - 5, 15 is the minuend, and 5 is the subtrahend.
  • Subtract the subtrahend from the minuend. For example, 15 - 5 equals 10.
  • The result is called the difference.

In more complex expressions, like our example problem, ensure that you follow the correct order of operations (PEMDAS) so that you don't subtract before completing any required multiplications, divisions, parentheses, or exponents first.
Multiplication
Multiplication is another fundamental arithmetic operation and is indicated by a times sign (脳) or an asterisk (*). Multiplying means combining equal groups. For instance:
  • If you have 5 groups of 3 apples, multiplication (5 * 3) shows that you have a total of 15 apples.
  • When two numbers are multiplied, the result is called the product.

In expressions like our example, where we have 15 - 5 脳 3, we need to perform the multiplication before the subtraction due to PEMDAS. So, 5 脳 3 equals 15. This simplifies our equation to 15 - 15, which then becomes 0. Always remember to multiply first unless there are parentheses indicating otherwise.

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