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Chapter 1: Problem 49

Simplify. \(32 \div 4-3\)

Short Answer

Expert verified
The simplified result is 5.

Step by step solution

01

Divide 32 by 4

To begin solving the expression, perform the division operation first. Divide 32 by 4 to simplify the first part of the expression. \[32 \div 4 = 8\]
02

Subtract 3 from 8

After the division, subtract 3 from the result of the division. \[8 - 3 = 5\]

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Key Concepts

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

Division in Arithmetic
Arithmetic division involves splitting a number into equal parts. In our exercise, this is shown as dividing 32 by 4. The division sign \(\div\) tells us to distribute 32 among 4 equal groups. When you divide 32 by 4, each group will contain 8, because 32 divided by 4 equals 8.

Understanding division helps in breaking down large problems into smaller, more manageable parts. It's one part of the broader order of operations that dictates solving expressions in particular steps. Division often comes before subtraction when simplifying mathematical expressions as shown in our problem with 32 divided by 4 first.

To make sure you understand division:
  • Think of it as sharing or grouping numbers equally.
  • Use division tables or calculators to check your answers.
  • Practice with different numbers to become more comfortable.
Subtraction in Arithmetic
Subtraction is the arithmetic process of taking one number away from another. It is symbolized by the minus sign \(-\). In the simplified expression, we subtract 3 from the result of the division (8). The subtraction gives us the final result, 5, because \(8 - 3 = 5\).

Subtraction reduces the quantity of the total. It is usually one of the last steps in operations when simplifying expressions. Knowing how to subtract correctly is essential in arithmetic as it affects the final outcome.

To better understand subtraction:
  • Visualize subtraction by imagining taking away items in real life scenarios.
  • Practice subtraction with different numbers, both small and large, to improve accuracy.
  • Double check your work by adding the subtracted number back to the result as a form of verification.
Simplifying Expressions
Simplifying expressions means reducing them to their simplest form. It involves following the order of operations, which includes division first, then subtraction, just like in our example. The order of operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) dictates the sequence to solve parts of an expression.

In the example \(32 \div 4 - 3\), simplifying involves performing division first to get 8, followed by subtraction, resulting in the final value of 5. Understanding how to simplify expressions is vital in mathematics as it ensures accurate results.

To improve simplification skills:
  • Always remember and apply the order of operations.
  • Work through examples step by step until you feel confident.
  • Check your completed work to make sure all steps are correctly followed.

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