Egypt Primary 6 Mathematics, Week 5: The parts of an expression: terms, coefficients and constants

Letters and the parts of expressions

Week 5 · Letters for unknowns and the parts of an expression · 3 lessons

The parts of an expression: terms, coefficients and constants

Discover Mathematics P6: Term 1, Unit 3, Lessons 1–2

GoalName the terms, coefficients, constants and like terms in an expression.

New words

term · one part of an expression, separated from the others by + or −coefficient · the number that multiplies the letter in a termconstant · a term with no letter; its value never changeslike terms · terms with the same letter, like 3x and 5x

Explanation

An expression is built from terms joined by + or −. In 4x + 9 there are two terms: 4x and 9. In the term 4x, the number 4 is the coefficient, because it multiplies the variable x. The term 9 has no letter, so it is a constant. A letter alone, like x, has coefficient 1, because x = 1x. Like terms have the same letter, so 3x and 5x are like terms, but 3x and 5y are not. Constants are also like each other. Like terms can be added together, which we use in later lessons.

In 4x + 9	What it is
4x	a term; 4 is the coefficient and x is the variable
9	a constant term (no letter)
+	joins the two terms

Worked examples

Term	Coefficient	Variable
4a	4	a
9	—	—

Parts of 4a + 9. Terms: 4a and 9. Coefficient: 4. Variable: a. Constant: 9.

Term	2x	3y	x	8
Coefficient	2	3	1	—

Look at 2x + 3y + x + 8. There are four terms: 2x, 3y, x and 8. The coefficients are 2, 3 and 1 (for x). The constant is 8. The like terms are 2x and x, because both have the letter x.

Group	Terms
m-terms	5m, 2m
Constants	3, 7
n-terms	4n

Sorting terms: 5m, 3, 2m, 7 and 4n. The m-terms are 5m and 2m, the constants are 3 and 7, and 4n is alone.

Class activity

Expression cards. Write terms on small cards: 3x, 8, 5x, 2y, 6, x. A grown-up shuffles them and the child sorts them into piles of like terms, then makes an expression by laying cards in a row with plus signs between them. Count the terms, name the constant and read each coefficient aloud.

Practice

In 7y + 2 name the coefficient, the variable and the constant.

How many terms does 3x + 4y + 5 have? Name them.

Which are the like terms in 6a + 2b + 4a + 9?

What is the coefficient of x in x + 6?

Are 5x and 5y like terms? Explain.