Problem 605 - Prealgebra

Question

Translate each phrase to math notation and then simplify. The difference of 32 and 18

Step-by-Step Solution

Answer

14

Step 1: Translate the phrase to math notation

The phrase 'The difference of 32 and 18' means to subtract 18 from 32. In mathematical notation, 'the difference of' indicates subtraction. Therefore, the expression is: \( 32 - 18 \)

Step 2: Simplify the expression

Perform the subtraction to simplify the expression: \( 32 - 18 = 14 \)

Key Concepts

Math Notation

Math notation is the language of mathematics. It uses symbols and expressions to convey mathematical ideas and operations. For subtraction, the symbol used is '-'. When you see 'the difference of' in a phrase, it means to subtract one number from another.
For example, take the exercise given: 'The difference of 32 and 18.' We translate this to math notation as:

• 32 - 18

This tells us to subtract 18 from 32. Understanding math notation is crucial because it helps us to clearly communicate mathematical operations and makes solving problems easier. Always look for key phrases like 'sum', 'product', 'difference', and 'quotient' to determine the operations needed.

Simplifying Expressions

Simplifying expressions means to perform the operations so that the expression is reduced to its simplest form. In our exercise, the expression is 32 - 18.
To simplify it, we simply perform the subtraction:

• 32 - 18 = 14

This means that the simplest form of the expression 'the difference of 32 and 18' is 14. Simplifying is important in math because it makes expressions easier to understand and work with. Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) to simplify effectively. In this case, since subtraction is the only operation, we directly subtract.

Basic Arithmetic

Basic arithmetic includes operations like addition, subtraction, multiplication, and division. These are the building blocks of all mathematics. In our exercise, we're dealing with subtraction.
Subtraction is taking away one number from another. Let's break it down:

• Start from the rightmost digit (units place).
• Subtract the digits column by column.
• Borrow from the next column if needed.

In the given problem:

• Subtract 8 from 2 - since 2 is smaller than 8, we borrow 1 from 3 (now 2).
• 12 - 8 = 4.
• 2 - 1 = 1.

So, we get 14.
Understanding and practicing basic arithmetic helps to build a strong foundation for more complex math topics.