G S Rehill's Interactive Maths Software Series - "Building a Strong Foundation in Mathematics" from mathsteacher.com.au.

 

Year 7 Interactive Maths - Second Edition


Expressions

An expression consists of terms that are written with arithmetical signs between them such as the addition, subtraction, division and multiplication signs.

4x + 6x is an example of an expression where 4x and 6x are called the terms of the expression.  2x - 3y is another example of an expression with two terms.


Like Terms

Terms with the same pronumeral (or pronumerals) are called like terms.

4x + 6x is an algebraic expression consisting of two like terms.  100x - 80x + 50x is an algebraic expression consisting of three like terms.


Unlike Terms

Terms with different pronumerals are called unlike terms.

4x + 6y is an algebraic expression consisting of two unlike terms.  100x - 80y + 50z is an algebraic expression consisting of three unlike terms.  10a + 5b + 7c is an algebraic expression consisting of three unlike terms.


Addition (or Subtraction) of Like Terms

Clearly, 5 dollars + 10 dollars = 15 dollars

If the dollars are represented by the pronumeral d, then the statement

5 dollars + 10 dollars = 15 dollars

can be described by

5d + 10d = 15d


From the above discussion, we can state that:

Only like terms can be added (or subtracted) to simplify an expression.

4a + 5a = 9a but 4a + 5b can not be added because the expression consists of the unlike terms 4a and 5b.

Likewise, 5a + 8a + 10c is an expression consisting of the two like terms 5a and 8a and the unlike term 10c.  So, we can simplify the statement 5a + 8a + 10c by adding the like terms, 5a +8a.  5a + 8a + 10c = 13a + 10c


Example 4

Solution:


Example 5

Solution:


Key Terms

expression, arithmetical signs, like terms, unlike terms, simplify an expression

 

Study Another Topic in Chapter 5: Algebra

Pronumerals ] Multiplication of a Pronumeral by a Number ] Multiplication of a Term by a Number ] [ Expressions ] Multiplication of Pronumerals ] Multiplication of Terms ] Further Like Terms ] Division of a Term by a Number ] The Distributive Law ] Symbols ] Index ]

 

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