Table of Contents
Subtraction is one of the fundamental operations in algebra. It represents the operation of removing objects from a collection. The result of a subtraction is called a "difference."
Definition
The subtraction of two numbers is the operation of finding the difference between them. If \( a $\)and \( b $\)are two numbers, the subtraction of \( b $\)from \( a $\)is written as \( a - b \).
Properties
- Subtraction is not commutative, i.e., \( a - b \neq b - a $\)in general.
- Subtraction is not associative, i.e., \( (a - b) - c \neq a - (b - c) $\)in general.
Examples in Algebra
- If \( x = 10 $\)and \( y = 5 \), then \( x - y = 10 - 5 = 5 \).
- In terms of variables, \( a - b $\)simply represents the difference between \( a $\)and \( b \).
R Programming Examples
# Example 1: Subtraction of two numbers
a <- 10
b <- 5
difference <- a - b
print(difference)
# Example 2: Subtraction with variables
x <- 15
y <- 7
result <- x - y
print(result)
Practice
- If \( a = 8 $\)and \( b = 3 \), what is \( a - b \)?
- Find the difference between \( x $\)and \( 2x \).
In this expression, \( x $\)and \( 2x $\)are like terms because they both have \( x $\)as the variable part. To combine them, we add their coefficients (keeping in mind the signs). The coefficient of \( x $\)is 1 (since \( x $\)is the same as \( 1x \)).
\( x \), or explicitly \( 1x \),can be read a "one quantity of X", so the practice problem can be read as "the subtraction of 2 quantities of \( x $\)from 1 quantity of \( x \)".
- Find the difference between \( 1x $\)and \( x \)