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Chapter 1: Problem 226

Simplify. $$ \text { (a) } 35-16 \text { (b) } 35+(-16) $$

Short Answer

Expert verified
(a) 19 (b) 19

Step by step solution

01

Problem Overview

There are two parts to simplify: (a) 35 - 16 and (b) 35 + (-16).
02

Simplify Part (a)

The expression is 35 - 16. Subtract 16 from 35. \[ 35 - 16 = 19 \]
03

Simplify Part (b)

The expression is 35 + (-16). Adding a negative number is the same as subtracting the positive value. Thus, 35 + (-16) is the same as 35 - 16. \[ 35 + (-16) = 19 \]

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Key Concepts

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

subtraction
Subtraction is a basic arithmetic operation where you take one number away from another. This operation is essential in everyday life and math.
When you subtract, you find the difference between two numbers. For example, in part (a) of the exercise, you have to find the difference between 35 and 16.
The mathematical expression is: \[ 35 - 16 \] To simplify this, you subtract 16 from 35, resulting in 19. The subtraction of 16 from 35 can be visualized on a number line, moving 16 steps left from 35, which brings you to 19.
Understanding subtraction is crucial as it lays the foundation for more complex math concepts like negative numbers and integer operations.
negative numbers
Negative numbers are numbers less than zero, represented with a minus sign (鈭�). They play a significant role in various areas of math, including algebra and finance.
In part (b) of the exercise, the expression is: \[ 35 + (-16) \] Adding a negative number is the same as subtracting its positive counterpart. Hence, the expression \[ 35 + (-16) \] is equivalent to \[ 35 - 16 \], which simplifies to 19.
Understanding how negative numbers work can help you solve various problems more efficiently. They allow us to describe values less than zero, which is common in real-world scenarios like temperatures below freezing or debts in finance.
integer operations
Integer operations involve the addition, subtraction, multiplication, and division of whole numbers, both positive and negative.
When working with integers, especially in addition and subtraction, it's important to keep the sign in mind. Here's a quick guide to remember:
  • Adding two positive integers always gives a positive result.
  • Adding two negative integers always gives a negative result.
  • Adding a positive and a negative integer requires you to find the difference of their absolute values and keep the sign of the larger absolute value.
  • Subtracting an integer is like adding its opposite. For example, subtracting -3 is like adding 3.
In our exercise, we see this in action. For part (b), \[ 35 + (-16) \], the negative sign indicates subtraction. So, it simplifies to: \[ 35 - 16 \], which equals 19.
Mastering integer operations is essential for solving more complex problems in algebra and beyond.

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