A mathematical expression is any calculation or formula that involves a combination of numbers and/or variables, as well as operators. Make sure you are familiar with different names for these operators so we can work mathematically with these.
Let's start with some terminology that will help us identify different parts of a mathematical expression. Some of these we will already be familiar with, and some will be new.
Algebraic terms must have the EXACT SAME combination of variables to be like terms.
This picture summarises some of this terminology:
There are a few conventions that we make when writing algebraic expressions, some of which we have already been using.
The expression $2+1+8$2+1+8 represents the number of rockmelons, apples, and lemons in Caitlin's shopping trolley
a) What type of expression does $2+1+8$2+1+8 represent?
A) Sum B) Product C) Quotient D) Difference
Think: Which of these words means that the terms are added?
Do: This expression represents a sum.
b) How many terms does the expression have?
Think: Terms are separated by $+$+ and $-$− signs. How many numbers are being separated by the plus signs here?
Do: There are $3$3 terms in this expression.
The expression $7y$7y represents the total number of biscuits in $y$y packets if each packet contains $7$7 biscuits.
a) What type of expression does $7y$7y represent?
A) Product B) Quotient C) Difference D) Sum
Think: Which of these words means that the terms are multiplied?
Do: This expression is a product.
b) What are the factors in the expression?
Think: Factors are numbers or variables that are multiplied together to get a term.
Do: $7y$7y means $7\times y$7×y. So we can see that the factors in this expression are $7$7 and $y$y.
Rewrite the expression $z\div5$z÷5 without using a division sign.
Think: What conventions do we use in algebraic expressions?
Do: We can write expressions that involve division by using fractions. So $z\div5$z÷5 is the same as $\frac{z}{5}$z5.
Consider the expression $-5+3a-6+8a$−5+3a−6+8a.
a) How many terms are in the expression?
Think: Terms are separated by $+$+ and $-$− signs. Let's count them.
Do: There are $4$4 terms in this expression. (They are $-5$−5, $3a$3a, $-6$−6 and $8a$8a).
b) What is the first term?
Think: What term is written first in this expression?
Do: The first term is $-5$−5.
c) What are the like terms?
Think: Like terms are terms with exactly same variable parts.
Do: There are two pairs of like terms in this expression. The first pair of like terms is $-5$−5 and $-6$−6. The second pair of like terms is $3a$3a and $8a$8a.
d) What are the coefficients?
Think: Coefficients are numbers that come before variable factors.
Do: There are two coefficients in this expression: $3$3 and $8$8.
e) What are the constant terms?
Think: Constant terms are terms without any variables.
Do: There are two constants in this expression: $-5$−5 and $-6$−6.
The expression $n+9$n+9 represents nine more than the number of points, $n$n, scored by the opposition team in a basketball game.
a) What type of expression does $n+9$n+9 represent?
b) How many terms does the expression have?
c) What is the constant term?
The expression $8u+2$8u+2 represents the cost of a $u$u-minute international phone call, where $2$2 represents the connection cost.
a) How many terms are there in the expression?
b) What is the second term?
c) Identify the coefficient.
d) What is the constant term?