Year 7 Interactive Maths - Second Edition

Multiplication of a Pronumeral by a Number

Note:

When a number and a pronumeral are multiplied together, then the multiplication sign is usually omitted.

Example 1

Write the following in a simpler form:

Solution:

Note:

In part d above, we let 1m = m.  When you see a pronumeral like m without a number preceding it, the number 1 is understood to precede the pronumeral.

Note:

When multiplying numbers with pronumerals, we always write the numbers in front of the letters.

Example 2

Write the following in a simpler form:

Solution:

Coefficient of a Pronumeral

The number in front of the pronumeral represents how many lots of the pronumeral there are.   This number is said to be the coefficient of the pronumeral.

For example, in 10x the coefficient of x is 10 and in 5y the coefficient of y is 5.

Terms

The product of a number and a pronumeral forms a term.  Such a term is also known as an algebraic term.  Terms often include pronumerals but may also be a number called a constant term.

Examples of terms include 4a, c, 5, 9, 5b, 8p, 15q, 20r, 26, n, 14x, 40y, 56z and 28v.

Note the following:

• The product of a number and different pronumerals is also called a term.
  E.g. 4ab, 5bc, 8pqr, 14xy, 40yz, 56xyz and 28uv are all terms.
  
  
• The fraction formed by a number and a pronumeral or pronumerals is also called a term.

Example 3

State the coefficient of x in each of the following:
a.  12x
b.  25x

Solution:

a.  The coefficient of x is 12.
b.  The coefficient of x is 25.

Key Terms

coefficient of a pronumeral, term, algebraic term, constant